These are, 10, simulations of the Ball and Cell Game with, 1000, balls and , 1000, cells The, 1000, balls landed in the following cells [861, 759, 751, 890, 301, 992, 6, 994, 955, 300, 100, 550, 197, 283, 352, 17, 744, 741, 858, 763, 162, 274, 180, 312, 171, 595, 25, 602, 605, 828, 477, 398, 50, 379, 175, 8, 362, 174, 940, 393, 845, 187, 656, 897, 454, 77, 622, 39, 604, 583, 451, 718, 509, 239, 367, 51, 565, 396, 19, 447, 936, 346, 643, 817, 177, 707, 869, 357, 202, 474, 458, 155, 482, 584, 628, 751, 130, 585, 341, 297, 231, 772, 172, 781, 147, 266, 143, 704, 521, 762, 780, 765, 308, 256, 409, 759, 840, 361, 625, 90, 786, 683, 372, 183, 109, 40, 17, 454, 308, 337, 727, 930, 505, 213, 137, 873, 708, 339, 125, 447, 356, 454, 804, 676, 266, 296, 834, 87, 144, 866, 939, 309, 573, 47, 284, 459, 515, 901, 878, 743, 107, 779, 165, 112, 331, 772, 219, 150, 552, 314, 477, 226, 875, 11, 30, 646, 800, 296, 884, 920, 592, 864, 523, 535, 681, 948, 640, 58, 67, 754, 889, 977, 321, 965, 642, 548, 701, 596, 224, 990, 415, 209, 799, 310, 579, 241, 955, 743, 322, 140, 689, 357, 90, 35, 783, 922, 100, 886, 920, 904, 959, 846, 663, 494, 585, 662, 497, 160, 226, 265, 309, 515, 866, 581, 381, 131, 73, 216, 677, 444, 622, 350, 436, 16, 413, 563, 899, 745, 941, 451, 424, 839, 873, 842, 49, 956, 197, 249, 545, 158, 897, 979, 905, 361, 251, 64, 555, 185, 436, 702, 174, 639, 109, 972, 521, 498, 437, 421, 856, 753, 434, 873, 805, 716, 863, 648, 604, 765, 732, 898, 353, 812, 777, 286, 654, 877, 335, 503, 753, 841, 789, 334, 49, 477, 628, 527, 56, 581, 401, 661, 298, 149, 101, 261, 186, 3, 854, 246, 951, 225, 772, 348, 814, 498, 728, 930, 242, 196, 305, 701, 882, 277, 470, 554, 261, 501, 161, 205, 354, 1000, 186, 994, 741, 157, 321, 413, 640, 163, 121, 541, 546, 834, 940, 828, 723, 544, 597, 740, 324, 885, 443, 40, 460, 107, 732, 39, 913, 763, 562, 590, 660, 530, 146, 819, 492, 802, 118, 884, 590, 394, 564, 612, 13, 343, 781, 293, 988, 481, 581, 190, 422, 956, 430, 462, 61, 336, 131, 968, 304, 393, 809, 302, 78, 373, 419, 241, 889, 600, 847, 538, 923, 503, 204, 851, 183, 547, 584, 351, 127, 612, 894, 881, 183, 593, 509, 294, 88, 148, 16, 529, 452, 362, 975, 176, 762, 238, 963, 994, 342, 732, 458, 673, 439, 785, 749, 466, 665, 350, 664, 828, 458, 145, 270, 524, 762, 983, 591, 640, 960, 903, 581, 474, 851, 757, 885, 387, 560, 144, 84, 319, 809, 509, 821, 158, 300, 55, 853, 801, 806, 170, 473, 193, 942, 195, 421, 346, 879, 812, 254, 99, 405, 329, 700, 37, 929, 227, 658, 320, 280, 846, 301, 758, 66, 664, 101, 699, 879, 601, 991, 993, 700, 450, 207, 490, 874, 121, 118, 431, 110, 118, 416, 266, 879, 777, 559, 740, 393, 944, 232, 56, 679, 28, 102, 872, 761, 272, 40, 734, 17, 612, 440, 205, 945, 310, 163, 383, 490, 569, 747, 684, 292, 364, 399, 414, 16, 731, 178, 88, 98, 738, 567, 783, 233, 926, 806, 791, 311, 834, 450, 423, 1000, 451, 509, 574, 657, 1, 20, 654, 186, 107, 601, 358, 96, 105, 60, 105, 995, 616, 523, 302, 244, 531, 378, 490, 457, 222, 830, 219, 562, 537, 111, 180, 370, 556, 504, 364, 180, 755, 265, 308, 153, 288, 895, 351, 645, 269, 481, 636, 82, 860, 649, 4, 274, 150, 444, 795, 524, 48, 359, 270, 532, 254, 772, 990, 284, 852, 512, 89, 194, 617, 677, 762, 311, 553, 466, 439, 865, 992, 847, 788, 244, 710, 945, 552, 72, 53, 390, 608, 510, 387, 531, 478, 454, 341, 398, 319, 679, 139, 73, 623, 172, 49, 67, 248, 949, 719, 907, 432, 496, 157, 434, 661, 346, 673, 473, 811, 382, 860, 608, 280, 456, 960, 354, 676, 335, 787, 186, 220, 683, 276, 102, 219, 107, 124, 521, 340, 770, 714, 912, 397, 722, 291, 336, 301, 723, 292, 806, 782, 423, 725, 623, 690, 138, 293, 445, 898, 58, 771, 717, 790, 373, 569, 189, 222, 865, 692, 319, 11, 458, 158, 979, 644, 39, 999, 753, 951, 481, 738, 500, 859, 48, 407, 25, 635, 248, 841, 62, 342, 791, 892, 616, 317, 912, 483, 563, 687, 114, 242, 417, 755, 461, 501, 788, 339, 778, 369, 680, 784, 19, 40, 424, 462, 731, 111, 327, 331, 5, 846, 925, 630, 151, 977, 405, 902, 502, 758, 804, 730, 682, 453, 889, 73, 91, 101, 111, 172, 746, 300, 153, 37, 492, 293, 194, 228, 489, 189, 300, 429, 971, 99, 215, 721, 948, 731, 169, 469, 176, 843, 249, 74, 861, 476, 519, 971, 832, 153, 790, 289, 956, 213, 863, 64, 241, 355, 899, 363, 314, 283, 169, 489, 636, 466, 411, 994, 819, 698, 333, 885, 387, 943, 904, 882, 301, 611, 379, 17, 74, 135, 134, 854, 264, 522, 68, 501, 371, 488, 299, 705, 202, 694, 527, 584, 10, 329, 567, 376, 978, 307, 487, 564, 407, 44, 80, 535, 736, 607, 875, 85, 418, 69, 413, 966, 532, 748, 561, 907, 223, 359, 874, 928, 991, 373, 705, 20, 956, 828, 346, 167, 744, 204, 60, 786, 786, 799, 251, 615, 937, 217, 831, 142, 502, 305, 463, 20, 540, 904, 683, 666, 952, 47, 677, 603, 662, 81, 338, 823, 326, 685, 575, 762, 951, 597, 276, 316, 886, 164, 672, 692, 67, 167, 342, 950, 695, 194, 177, 709, 536, 752, 631, 580, 435, 608, 63, 66, 88, 877, 488, 163, 628, 363, 313, 322, 848, 178, 514, 526, 739, 626, 841, 841, 513, 531, 314, 642, 847, 841, 113, 370, 91, 504, 535, 833, 897, 329, 178, 637, 130, 373, 748, 291, 369, 188, 4, 33, 527, 406, 813, 804, 537, 506] The set of cells that are occupied is {1, 3, 4, 5, 6, 8, 10, 11, 13, 16, 17, 19, 20, 25, 28, 30, 33, 35, 37, 39, 40, 44, 47, 48, 49, 50, 51, 53, 55, 56, 58, 60, 61, 62, 63, 64, 66, 67, 68, 69, 72, 73, 74, 77, 78, 80, 81, 82, 84, 85, 87, 88, 89, 90, 91, 96, 98, 99, 100, 101, 102, 105, 107, 109, 110, 111, 112, 113, 114, 118, 121, 124, 125, 127, 130, 131, 134, 135, 137, 138, 139, 140, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 153, 155, 157, 158, 160, 161, 162, 163, 164, 165, 167, 169, 170, 171, 172, 174, 175, 176, 177, 178, 180, 183, 185, 186, 187, 188, 189, 190, 193, 194, 195, 196, 197, 202, 204, 205, 207, 209, 213, 215, 216, 217, 219, 220, 222, 223, 224, 225, 226, 227, 228, 231, 232, 233, 238, 239, 241, 242, 244, 246, 248, 249, 251, 254, 256, 261, 264, 265, 266, 269, 270, 272, 274, 276, 277, 280, 283, 284, 286, 288, 289, 291, 292, 293, 294, 296, 297, 298, 299, 300, 301, 302, 304, 305, 307, 308, 309, 310, 311, 312, 313, 314, 316, 317, 319, 320, 321, 322, 324, 326, 327, 329, 331, 333, 334, 335, 336, 337, 338, 339, 340, 341, 342, 343, 346, 348, 350, 351, 352, 353, 354, 355, 356, 357, 358, 359, 361, 362, 363, 364, 367, 369, 370, 371, 372, 373, 376, 378, 379, 381, 382, 383, 387, 390, 393, 394, 396, 397, 398, 399, 401, 405, 406, 407, 409, 411, 413, 414, 415, 416, 417, 418, 419, 421, 422, 423, 424, 429, 430, 431, 432, 434, 435, 436, 437, 439, 440, 443, 444, 445, 447, 450, 451, 452, 453, 454, 456, 457, 458, 459, 460, 461, 462, 463, 466, 469, 470, 473, 474, 476, 477, 478, 481, 482, 483, 487, 488, 489, 490, 492, 494, 496, 497, 498, 500, 501, 502, 503, 504, 505, 506, 509, 510, 512, 513, 514, 515, 519, 521, 522, 523, 524, 526, 527, 529, 530, 531, 532, 535, 536, 537, 538, 540, 541, 544, 545, 546, 547, 548, 550, 552, 553, 554, 555, 556, 559, 560, 561, 562, 563, 564, 565, 567, 569, 573, 574, 575, 579, 580, 581, 583, 584, 585, 590, 591, 592, 593, 595, 596, 597, 600, 601, 602, 603, 604, 605, 607, 608, 611, 612, 615, 616, 617, 622, 623, 625, 626, 628, 630, 631, 635, 636, 637, 639, 640, 642, 643, 644, 645, 646, 648, 649, 654, 656, 657, 658, 660, 661, 662, 663, 664, 665, 666, 672, 673, 676, 677, 679, 680, 681, 682, 683, 684, 685, 687, 689, 690, 692, 694, 695, 698, 699, 700, 701, 702, 704, 705, 707, 708, 709, 710, 714, 716, 717, 718, 719, 721, 722, 723, 725, 727, 728, 730, 731, 732, 734, 736, 738, 739, 740, 741, 743, 744, 745, 746, 747, 748, 749, 751, 752, 753, 754, 755, 757, 758, 759, 761, 762, 763, 765, 770, 771, 772, 777, 778, 779, 780, 781, 782, 783, 784, 785, 786, 787, 788, 789, 790, 791, 795, 799, 800, 801, 802, 804, 805, 806, 809, 811, 812, 813, 814, 817, 819, 821, 823, 828, 830, 831, 832, 833, 834, 839, 840, 841, 842, 843, 845, 846, 847, 848, 851, 852, 853, 854, 856, 858, 859, 860, 861, 863, 864, 865, 866, 869, 872, 873, 874, 875, 877, 878, 879, 881, 882, 884, 885, 886, 889, 890, 892, 894, 895, 897, 898, 899, 901, 902, 903, 904, 905, 907, 912, 913, 920, 922, 923, 925, 926, 928, 929, 930, 936, 937, 939, 940, 941, 942, 943, 944, 945, 948, 949, 950, 951, 952, 955, 956, 959, 960, 963, 965, 966, 968, 971, 972, 975, 977, 978, 979, 983, 988, 990, 991, 992, 993, 994, 995, 999, 1000} The set of cells that have exactly one ball in them is {1, 3, 5, 6, 8, 10, 13, 28, 30, 33, 35, 44, 50, 51, 53, 55, 61, 62, 63, 68, 69, 72, 77, 78, 80, 81, 82, 84, 85, 87, 89, 96, 98, 110, 112, 113, 114, 124, 125, 127, 134, 135, 137, 138, 139, 140, 142, 143, 145, 146, 147, 148, 149, 151, 155, 160, 161, 162, 164, 165, 170, 171, 175, 185, 187, 188, 190, 193, 195, 196, 207, 209, 215, 216, 217, 220, 223, 224, 225, 227, 228, 231, 232, 233, 238, 239, 246, 256, 264, 269, 272, 277, 286, 288, 289, 294, 297, 298, 299, 304, 307, 312, 313, 316, 317, 320, 324, 326, 327, 333, 334, 337, 338, 340, 343, 348, 352, 353, 355, 356, 358, 367, 371, 372, 376, 378, 381, 382, 383, 390, 394, 396, 397, 399, 401, 406, 409, 411, 414, 415, 416, 417, 418, 419, 422, 429, 430, 431, 432, 435, 437, 440, 443, 445, 452, 453, 456, 457, 459, 460, 461, 463, 469, 470, 476, 478, 482, 483, 487, 494, 496, 497, 500, 505, 506, 510, 512, 513, 514, 519, 522, 526, 529, 530, 536, 538, 540, 541, 544, 545, 546, 547, 548, 550, 553, 554, 555, 556, 559, 560, 561, 565, 573, 574, 575, 579, 580, 583, 591, 592, 593, 595, 596, 600, 602, 603, 605, 607, 611, 615, 617, 625, 626, 630, 631, 635, 637, 639, 643, 644, 645, 646, 648, 649, 656, 657, 658, 660, 663, 665, 666, 672, 680, 681, 682, 684, 685, 687, 689, 690, 694, 695, 698, 699, 702, 704, 707, 708, 709, 710, 714, 716, 717, 718, 719, 721, 722, 725, 727, 728, 730, 734, 736, 739, 745, 746, 747, 749, 752, 754, 757, 761, 770, 771, 778, 779, 780, 782, 784, 785, 787, 789, 795, 800, 801, 802, 805, 811, 813, 814, 817, 821, 823, 830, 831, 832, 833, 839, 840, 842, 843, 845, 848, 852, 853, 856, 858, 859, 864, 869, 872, 878, 881, 890, 892, 894, 895, 901, 902, 903, 905, 913, 922, 923, 925, 926, 928, 929, 936, 937, 939, 941, 942, 943, 944, 949, 950, 952, 959, 963, 965, 966, 968, 972, 975, 978, 983, 988, 993, 995, 999} We remove these balls and are now left with, 639, balls The, 639, balls landed in the following cells [702, 788, 975, 447, 136, 782, 965, 612, 758, 316, 148, 856, 268, 43, 281, 285, 121, 231, 528, 243, 565, 163, 511, 121, 290, 588, 268, 979, 595, 68, 317, 793, 438, 775, 470, 81, 871, 933, 260, 350, 613, 869, 674, 508, 716, 843, 810, 290, 924, 615, 149, 944, 258, 660, 589, 190, 337, 387, 171, 75, 158, 646, 668, 784, 94, 750, 302, 140, 194, 69, 625, 236, 621, 117, 807, 761, 871, 113, 328, 707, 126, 1000, 142, 426, 914, 3, 992, 460, 379, 774, 541, 804, 539, 352, 20, 77, 323, 512, 559, 472, 449, 718, 68, 686, 284, 90, 403, 234, 571, 988, 231, 217, 958, 160, 897, 69, 664, 857, 6, 298, 147, 721, 196, 483, 16, 675, 841, 257, 385, 902, 916, 495, 469, 436, 211, 927, 192, 825, 743, 964, 357, 697, 419, 690, 50, 538, 407, 41, 438, 599, 291, 252, 390, 479, 514, 379, 103, 163, 544, 212, 302, 79, 504, 16, 892, 929, 394, 143, 86, 42, 977, 618, 127, 988, 930, 777, 640, 305, 25, 587, 574, 68, 102, 204, 226, 8, 198, 499, 688, 813, 549, 888, 970, 97, 1, 519, 551, 94, 654, 104, 597, 668, 895, 868, 520, 449, 566, 299, 927, 14, 215, 144, 868, 576, 245, 964, 953, 777, 798, 257, 610, 105, 212, 456, 304, 574, 660, 315, 398, 54, 134, 696, 190, 311, 350, 922, 771, 346, 646, 193, 701, 348, 604, 620, 303, 819, 65, 30, 657, 823, 60, 571, 531, 604, 184, 805, 361, 389, 298, 63, 515, 975, 766, 886, 626, 736, 884, 357, 563, 98, 336, 653, 399, 16, 528, 70, 182, 170, 166, 886, 192, 24, 283, 744, 202, 784, 126, 428, 305, 743, 531, 62, 532, 290, 655, 740, 546, 512, 577, 588, 220, 878, 639, 813, 320, 536, 72, 211, 470, 224, 260, 943, 184, 699, 244, 590, 661, 489, 708, 669, 711, 728, 185, 336, 932, 173, 413, 539, 515, 709, 411, 611, 650, 201, 221, 784, 620, 294, 144, 147, 603, 799, 174, 517, 340, 214, 924, 977, 729, 707, 176, 535, 116, 397, 512, 163, 833, 833, 538, 238, 336, 739, 664, 751, 969, 149, 167, 854, 674, 235, 581, 341, 468, 424, 852, 806, 100, 234, 381, 120, 909, 957, 862, 511, 516, 671, 401, 820, 32, 477, 849, 659, 272, 537, 89, 553, 568, 432, 714, 531, 675, 714, 545, 398, 20, 494, 236, 631, 512, 658, 639, 135, 645, 136, 159, 749, 736, 554, 182, 247, 708, 66, 329, 381, 873, 696, 210, 837, 954, 310, 44, 246, 928, 817, 165, 474, 914, 842, 550, 612, 622, 797, 49, 285, 980, 286, 932, 193, 369, 534, 477, 173, 478, 435, 851, 493, 374, 455, 262, 429, 592, 578, 791, 784, 264, 445, 249, 906, 331, 469, 204, 716, 493, 536, 364, 971, 97, 369, 310, 909, 966, 975, 528, 242, 902, 822, 307, 798, 279, 139, 670, 525, 422, 912, 956, 735, 592, 528, 77, 168, 258, 430, 853, 612, 971, 96, 390, 638, 522, 367, 127, 395, 64, 931, 903, 884, 924, 283, 866, 172, 792, 696, 635, 269, 381, 118, 130, 919, 225, 59, 690, 501, 542, 374, 756, 258, 997, 358, 515, 382, 367, 440, 959, 859, 562, 632, 371, 755, 255, 279, 571, 655, 666, 732, 744, 318, 901, 741, 550, 389, 121, 63, 88, 990, 231, 716, 813, 236, 974, 897, 77, 423, 418, 532, 47, 888, 755, 451, 753, 592, 793, 404, 416, 595, 82, 442, 225, 333, 558, 571, 457, 139, 365, 623, 257, 792, 204, 520, 851, 38, 604, 238, 19, 836, 702, 485, 565, 367, 894, 98, 304, 485, 870, 890, 533, 390, 460, 239, 282, 864, 905, 189, 546, 114, 127, 645, 968, 608, 300, 413, 640, 531, 754, 637, 944, 625, 27, 646, 111] The set of cells that are occupied is {1, 3, 6, 8, 14, 16, 19, 20, 24, 25, 27, 30, 32, 38, 41, 42, 43, 44, 47, 49, 50, 54, 59, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 75, 77, 79, 81, 82, 86, 88, 89, 90, 94, 96, 97, 98, 100, 102, 103, 104, 105, 111, 113, 114, 116, 117, 118, 120, 121, 126, 127, 130, 134, 135, 136, 139, 140, 142, 143, 144, 147, 148, 149, 158, 159, 160, 163, 165, 166, 167, 168, 170, 171, 172, 173, 174, 176, 182, 184, 185, 189, 190, 192, 193, 194, 196, 198, 201, 202, 204, 210, 211, 212, 214, 215, 217, 220, 221, 224, 225, 226, 231, 234, 235, 236, 238, 239, 242, 243, 244, 245, 246, 247, 249, 252, 255, 257, 258, 260, 262, 264, 268, 269, 272, 279, 281, 282, 283, 284, 285, 286, 290, 291, 294, 298, 299, 300, 302, 303, 304, 305, 307, 310, 311, 315, 316, 317, 318, 320, 323, 328, 329, 331, 333, 336, 337, 340, 341, 346, 348, 350, 352, 357, 358, 361, 364, 365, 367, 369, 371, 374, 379, 381, 382, 385, 387, 389, 390, 394, 395, 397, 398, 399, 401, 403, 404, 407, 411, 413, 416, 418, 419, 422, 423, 424, 426, 428, 429, 430, 432, 435, 436, 438, 440, 442, 445, 447, 449, 451, 455, 456, 457, 460, 468, 469, 470, 472, 474, 477, 478, 479, 483, 485, 489, 493, 494, 495, 499, 501, 504, 508, 511, 512, 514, 515, 516, 517, 519, 520, 522, 525, 528, 531, 532, 533, 534, 535, 536, 537, 538, 539, 541, 542, 544, 545, 546, 549, 550, 551, 553, 554, 558, 559, 562, 563, 565, 566, 568, 571, 574, 576, 577, 578, 581, 587, 588, 589, 590, 592, 595, 597, 599, 603, 604, 608, 610, 611, 612, 613, 615, 618, 620, 621, 622, 623, 625, 626, 631, 632, 635, 637, 638, 639, 640, 645, 646, 650, 653, 654, 655, 657, 658, 659, 660, 661, 664, 666, 668, 669, 670, 671, 674, 675, 686, 688, 690, 696, 697, 699, 701, 702, 707, 708, 709, 711, 714, 716, 718, 721, 728, 729, 732, 735, 736, 739, 740, 741, 743, 744, 749, 750, 751, 753, 754, 755, 756, 758, 761, 766, 771, 774, 775, 777, 782, 784, 788, 791, 792, 793, 797, 798, 799, 804, 805, 806, 807, 810, 813, 817, 819, 820, 822, 823, 825, 833, 836, 837, 841, 842, 843, 849, 851, 852, 853, 854, 856, 857, 859, 862, 864, 866, 868, 869, 870, 871, 873, 878, 884, 886, 888, 890, 892, 894, 895, 897, 901, 902, 903, 905, 906, 909, 912, 914, 916, 919, 922, 924, 927, 928, 929, 930, 931, 932, 933, 943, 944, 953, 954, 956, 957, 958, 959, 964, 965, 966, 968, 969, 970, 971, 974, 975, 977, 979, 980, 988, 990, 992, 997, 1000} The set of cells that have exactly one ball in them is {1, 3, 6, 8, 14, 19, 24, 25, 27, 30, 32, 38, 41, 42, 43, 44, 47, 49, 50, 54, 59, 60, 62, 64, 65, 66, 70, 72, 75, 79, 81, 82, 86, 88, 89, 90, 96, 100, 102, 103, 104, 105, 111, 113, 114, 116, 117, 118, 120, 130, 134, 135, 140, 142, 143, 148, 158, 159, 160, 165, 166, 167, 168, 170, 171, 172, 174, 176, 185, 189, 194, 196, 198, 201, 202, 210, 214, 215, 217, 220, 221, 224, 226, 235, 239, 242, 243, 244, 245, 246, 247, 249, 252, 255, 262, 264, 269, 272, 281, 282, 284, 286, 291, 294, 299, 300, 303, 307, 311, 315, 316, 317, 318, 320, 323, 328, 329, 331, 333, 337, 340, 341, 346, 348, 352, 358, 361, 364, 365, 371, 382, 385, 387, 394, 395, 397, 399, 401, 403, 404, 407, 411, 416, 418, 419, 422, 423, 424, 426, 428, 429, 430, 432, 435, 436, 440, 442, 445, 447, 451, 455, 456, 457, 468, 472, 474, 478, 479, 483, 489, 494, 495, 499, 501, 504, 508, 514, 516, 517, 519, 522, 525, 533, 534, 535, 537, 541, 542, 544, 545, 549, 551, 553, 554, 558, 559, 562, 563, 566, 568, 576, 577, 578, 581, 587, 589, 590, 597, 599, 603, 608, 610, 611, 613, 615, 618, 621, 622, 623, 626, 631, 632, 635, 637, 638, 650, 653, 654, 657, 658, 659, 661, 666, 669, 670, 671, 686, 688, 697, 699, 701, 709, 711, 718, 721, 728, 729, 732, 735, 739, 740, 741, 749, 750, 751, 753, 754, 756, 758, 761, 766, 771, 774, 775, 782, 788, 791, 797, 799, 804, 805, 806, 807, 810, 817, 819, 820, 822, 823, 825, 836, 837, 841, 842, 843, 849, 852, 853, 854, 856, 857, 859, 862, 864, 866, 869, 870, 873, 878, 890, 892, 894, 895, 901, 903, 905, 906, 912, 916, 919, 922, 928, 929, 930, 931, 933, 943, 953, 954, 956, 957, 958, 959, 965, 966, 968, 969, 970, 974, 979, 980, 990, 992, 997, 1000} We remove these balls and are now left with, 304, balls The, 304, balls landed in the following cells [509, 308, 88, 396, 56, 548, 93, 596, 52, 768, 552, 951, 735, 16, 877, 158, 564, 146, 949, 724, 852, 596, 464, 377, 33, 728, 56, 681, 691, 269, 616, 29, 991, 242, 654, 852, 449, 235, 741, 348, 697, 210, 260, 721, 379, 813, 549, 611, 956, 786, 683, 64, 363, 353, 501, 526, 177, 243, 527, 117, 696, 214, 277, 366, 742, 243, 814, 793, 723, 102, 389, 533, 219, 535, 840, 400, 285, 995, 522, 138, 247, 38, 922, 328, 914, 173, 616, 759, 450, 219, 99, 890, 659, 717, 715, 270, 434, 911, 674, 400, 845, 870, 10, 653, 994, 951, 904, 482, 879, 641, 821, 534, 19, 637, 721, 562, 450, 477, 495, 338, 450, 287, 845, 738, 389, 613, 573, 711, 500, 66, 1000, 615, 571, 972, 875, 739, 792, 630, 519, 897, 426, 857, 744, 921, 429, 731, 197, 870, 732, 6, 932, 896, 229, 295, 714, 169, 225, 815, 553, 640, 971, 754, 85, 529, 353, 671, 508, 713, 405, 712, 256, 360, 367, 208, 617, 456, 19, 760, 92, 91, 707, 363, 310, 443, 706, 685, 193, 865, 329, 156, 426, 172, 831, 741, 80, 511, 179, 534, 865, 194, 898, 403, 149, 776, 999, 993, 426, 228, 643, 606, 717, 269, 994, 606, 572, 99, 730, 268, 42, 819, 935, 189, 887, 965, 938, 379, 174, 89, 123, 594, 761, 180, 801, 799, 270, 372, 639, 209, 418, 185, 983, 311, 151, 330, 914, 469, 58, 727, 296, 199, 93, 452, 142, 822, 867, 274, 112, 817, 660, 907, 320, 588, 345, 103, 42, 849, 834, 596, 605, 922, 935, 767, 914, 805, 774, 57, 107, 337, 978, 783, 559, 349, 609, 177, 48, 233, 718, 13, 551, 715, 131, 298, 131, 949, 239, 977, 1000, 719, 715, 976, 132, 417, 765, 214] The set of cells that are occupied is {6, 10, 13, 16, 19, 29, 33, 38, 42, 48, 52, 56, 57, 58, 64, 66, 80, 85, 88, 89, 91, 92, 93, 99, 102, 103, 107, 112, 117, 123, 131, 132, 138, 142, 146, 149, 151, 156, 158, 169, 172, 173, 174, 177, 179, 180, 185, 189, 193, 194, 197, 199, 208, 209, 210, 214, 219, 225, 228, 229, 233, 235, 239, 242, 243, 247, 256, 260, 268, 269, 270, 274, 277, 285, 287, 295, 296, 298, 308, 310, 311, 320, 328, 329, 330, 337, 338, 345, 348, 349, 353, 360, 363, 366, 367, 372, 377, 379, 389, 396, 400, 403, 405, 417, 418, 426, 429, 434, 443, 449, 450, 452, 456, 464, 469, 477, 482, 495, 500, 501, 508, 509, 511, 519, 522, 526, 527, 529, 533, 534, 535, 548, 549, 551, 552, 553, 559, 562, 564, 571, 572, 573, 588, 594, 596, 605, 606, 609, 611, 613, 615, 616, 617, 630, 637, 639, 640, 641, 643, 653, 654, 659, 660, 671, 674, 681, 683, 685, 691, 696, 697, 706, 707, 711, 712, 713, 714, 715, 717, 718, 719, 721, 723, 724, 727, 728, 730, 731, 732, 735, 738, 739, 741, 742, 744, 754, 759, 760, 761, 765, 767, 768, 774, 776, 783, 786, 792, 793, 799, 801, 805, 813, 814, 815, 817, 819, 821, 822, 831, 834, 840, 845, 849, 852, 857, 865, 867, 870, 875, 877, 879, 887, 890, 896, 897, 898, 904, 907, 911, 914, 921, 922, 932, 935, 938, 949, 951, 956, 965, 971, 972, 976, 977, 978, 983, 991, 993, 994, 995, 999, 1000} The set of cells that have exactly one ball in them is {6, 10, 13, 16, 29, 33, 38, 48, 52, 57, 58, 64, 66, 80, 85, 88, 89, 91, 92, 102, 103, 107, 112, 117, 123, 132, 138, 142, 146, 149, 151, 156, 158, 169, 172, 173, 174, 179, 180, 185, 189, 193, 194, 197, 199, 208, 209, 210, 225, 228, 229, 233, 235, 239, 242, 247, 256, 260, 268, 274, 277, 285, 287, 295, 296, 298, 308, 310, 311, 320, 328, 329, 330, 337, 338, 345, 348, 349, 360, 366, 367, 372, 377, 396, 403, 405, 417, 418, 429, 434, 443, 449, 452, 456, 464, 469, 477, 482, 495, 500, 501, 508, 509, 511, 519, 522, 526, 527, 529, 533, 535, 548, 549, 551, 552, 553, 559, 562, 564, 571, 572, 573, 588, 594, 605, 609, 611, 613, 615, 617, 630, 637, 639, 640, 641, 643, 653, 654, 659, 660, 671, 674, 681, 683, 685, 691, 696, 697, 706, 707, 711, 712, 713, 714, 718, 719, 723, 724, 727, 728, 730, 731, 732, 735, 738, 739, 742, 744, 754, 759, 760, 761, 765, 767, 768, 774, 776, 783, 786, 792, 793, 799, 801, 805, 813, 814, 815, 817, 819, 821, 822, 831, 834, 840, 849, 857, 867, 875, 877, 879, 887, 890, 896, 897, 898, 904, 907, 911, 921, 932, 938, 956, 965, 971, 972, 976, 977, 978, 983, 991, 993, 995, 999} We remove these balls and are now left with, 81, balls The, 81, balls landed in the following cells [539, 886, 87, 714, 948, 121, 667, 236, 982, 666, 480, 191, 134, 546, 468, 446, 773, 848, 217, 817, 26, 425, 157, 141, 887, 699, 300, 47, 705, 168, 981, 792, 232, 812, 378, 583, 532, 125, 955, 716, 818, 839, 914, 518, 976, 113, 163, 916, 652, 672, 824, 260, 4, 369, 365, 124, 397, 186, 974, 88, 490, 399, 272, 138, 746, 51, 173, 422, 642, 102, 121, 807, 770, 639, 520, 962, 829, 923, 98, 371, 548] The set of cells that are occupied is {4, 26, 47, 51, 87, 88, 98, 102, 113, 121, 124, 125, 134, 138, 141, 157, 163, 168, 173, 186, 191, 217, 232, 236, 260, 272, 300, 365, 369, 371, 378, 397, 399, 422, 425, 446, 468, 480, 490, 518, 520, 532, 539, 546, 548, 583, 639, 642, 652, 666, 667, 672, 699, 705, 714, 716, 746, 770, 773, 792, 807, 812, 817, 818, 824, 829, 839, 848, 886, 887, 914, 916, 923, 948, 955, 962, 974, 976, 981, 982} The set of cells that have exactly one ball in them is {4, 26, 47, 51, 87, 88, 98, 102, 113, 124, 125, 134, 138, 141, 157, 163, 168, 173, 186, 191, 217, 232, 236, 260, 272, 300, 365, 369, 371, 378, 397, 399, 422, 425, 446, 468, 480, 490, 518, 520, 532, 539, 546, 548, 583, 639, 642, 652, 666, 667, 672, 699, 705, 714, 716, 746, 770, 773, 792, 807, 812, 817, 818, 824, 829, 839, 848, 886, 887, 914, 916, 923, 948, 955, 962, 974, 976, 981, 982} We remove these balls and are now left with, 2, balls The, 2, balls landed in the following cells [379, 877] The set of cells that are occupied is {379, 877} The set of cells that have exactly one ball in them is {379, 877} We remove these balls and are now left with, 0, balls This took, 5, rounds The, 1000, balls landed in the following cells [95, 664, 342, 749, 237, 315, 777, 353, 386, 627, 1000, 628, 165, 60, 466, 554, 291, 731, 850, 322, 111, 641, 982, 602, 358, 408, 460, 299, 321, 764, 330, 921, 449, 263, 992, 611, 302, 737, 97, 219, 37, 338, 39, 337, 831, 675, 652, 858, 929, 706, 786, 460, 923, 127, 79, 33, 333, 247, 280, 853, 898, 400, 762, 931, 576, 78, 904, 228, 162, 714, 660, 602, 94, 493, 529, 147, 808, 973, 880, 90, 516, 906, 990, 468, 63, 251, 438, 875, 10, 83, 457, 335, 773, 908, 265, 264, 465, 529, 553, 570, 589, 606, 336, 308, 11, 974, 925, 572, 977, 652, 418, 762, 434, 760, 469, 549, 495, 302, 748, 275, 501, 205, 559, 697, 706, 218, 748, 353, 451, 385, 163, 649, 832, 69, 401, 824, 100, 354, 723, 402, 616, 662, 673, 513, 253, 495, 484, 208, 765, 335, 503, 302, 135, 441, 460, 235, 614, 940, 819, 881, 214, 597, 856, 635, 290, 962, 965, 865, 847, 557, 197, 742, 798, 263, 185, 696, 752, 618, 194, 108, 699, 843, 709, 294, 551, 142, 320, 419, 963, 951, 937, 167, 219, 687, 628, 775, 598, 536, 673, 221, 470, 876, 664, 786, 736, 784, 951, 685, 861, 246, 366, 577, 970, 671, 741, 492, 813, 107, 250, 193, 189, 256, 934, 188, 44, 116, 352, 878, 963, 125, 793, 943, 190, 112, 272, 196, 122, 220, 922, 306, 726, 291, 741, 38, 319, 306, 742, 5, 950, 721, 125, 402, 243, 249, 999, 770, 89, 864, 26, 936, 422, 750, 17, 593, 603, 473, 50, 733, 343, 607, 653, 365, 983, 359, 242, 102, 611, 992, 759, 561, 223, 449, 13, 919, 669, 228, 108, 531, 632, 212, 331, 188, 682, 53, 230, 954, 614, 290, 800, 689, 513, 931, 625, 602, 804, 672, 181, 19, 824, 992, 890, 520, 423, 780, 456, 706, 96, 760, 554, 1000, 51, 953, 938, 816, 334, 772, 500, 365, 961, 693, 116, 754, 954, 535, 951, 622, 834, 998, 43, 659, 16, 120, 327, 923, 11, 10, 731, 73, 225, 991, 294, 282, 386, 582, 735, 912, 1000, 526, 563, 353, 979, 525, 711, 49, 528, 886, 142, 710, 29, 457, 248, 535, 844, 515, 767, 140, 950, 933, 575, 292, 715, 800, 227, 376, 118, 894, 35, 409, 160, 535, 570, 919, 803, 353, 555, 427, 16, 843, 282, 211, 536, 425, 724, 138, 495, 429, 822, 994, 643, 303, 952, 649, 634, 160, 238, 936, 381, 598, 13, 249, 12, 879, 810, 53, 110, 871, 631, 956, 709, 398, 223, 568, 575, 530, 44, 135, 382, 543, 890, 740, 17, 157, 118, 524, 768, 367, 150, 515, 697, 311, 963, 475, 779, 419, 344, 309, 714, 919, 984, 453, 277, 775, 182, 968, 731, 122, 821, 427, 715, 946, 396, 39, 950, 35, 647, 760, 151, 447, 305, 112, 221, 930, 660, 795, 980, 24, 777, 509, 648, 883, 114, 391, 691, 157, 923, 329, 655, 161, 491, 82, 686, 292, 879, 987, 609, 905, 880, 656, 443, 944, 727, 479, 533, 816, 402, 525, 344, 301, 144, 274, 105, 137, 336, 261, 613, 589, 288, 992, 965, 852, 790, 113, 230, 829, 826, 494, 899, 574, 252, 555, 454, 491, 769, 597, 450, 290, 113, 730, 948, 1, 313, 15, 574, 271, 705, 503, 911, 859, 250, 871, 329, 610, 447, 345, 563, 742, 299, 593, 249, 874, 397, 853, 842, 473, 361, 871, 307, 439, 835, 292, 106, 176, 740, 776, 584, 232, 62, 452, 561, 156, 424, 776, 775, 297, 38, 210, 180, 254, 624, 254, 495, 370, 26, 849, 533, 929, 699, 366, 634, 714, 860, 251, 656, 455, 644, 977, 322, 199, 952, 212, 6, 582, 676, 704, 457, 974, 582, 953, 445, 59, 33, 772, 769, 139, 965, 109, 769, 267, 980, 563, 803, 831, 161, 438, 511, 270, 924, 76, 375, 310, 970, 865, 611, 28, 523, 744, 469, 383, 650, 939, 421, 856, 650, 658, 500, 107, 696, 78, 295, 874, 495, 72, 627, 60, 396, 689, 275, 905, 714, 840, 198, 645, 870, 461, 933, 123, 86, 274, 935, 950, 110, 154, 628, 159, 637, 944, 559, 303, 945, 457, 263, 403, 258, 153, 146, 107, 302, 163, 248, 920, 832, 811, 599, 911, 658, 878, 32, 86, 498, 77, 727, 407, 631, 886, 926, 401, 711, 192, 750, 507, 959, 276, 411, 132, 889, 564, 334, 794, 904, 300, 928, 540, 240, 535, 446, 939, 998, 209, 848, 184, 872, 364, 8, 720, 261, 664, 591, 797, 412, 719, 916, 962, 258, 252, 875, 67, 428, 196, 915, 730, 683, 943, 18, 878, 778, 37, 53, 716, 856, 70, 113, 580, 965, 198, 741, 236, 767, 538, 608, 623, 702, 945, 735, 336, 893, 8, 588, 377, 385, 274, 875, 124, 458, 469, 886, 211, 687, 68, 958, 26, 727, 738, 895, 46, 97, 741, 19, 549, 81, 890, 819, 67, 611, 922, 474, 980, 706, 800, 598, 999, 463, 892, 616, 607, 477, 922, 516, 245, 708, 341, 948, 354, 782, 537, 843, 110, 31, 808, 5, 809, 262, 393, 426, 722, 726, 409, 599, 579, 371, 573, 378, 135, 453, 414, 291, 10, 813, 987, 69, 820, 704, 350, 777, 973, 557, 713, 62, 257, 521, 915, 365, 766, 474, 591, 778, 84, 993, 564, 910, 100, 49, 846, 703, 401, 470, 133, 606, 375, 909, 654, 512, 509, 759, 148, 617, 347, 634, 481, 711, 229, 369, 626, 104, 97, 35, 949, 635, 967, 532, 205, 120, 753, 707, 322, 711, 511, 854, 169, 731, 696, 893, 784, 180, 584, 324, 193, 539, 859, 916, 90, 999, 794, 868, 34, 384, 468, 597, 228, 253, 491, 59, 957, 336, 319, 674, 778, 333, 305, 905, 896, 132, 506, 797, 945, 167, 716, 339, 164, 787, 981, 653, 433, 6, 507, 157, 931, 905, 639, 711, 47, 998, 477, 111, 545, 544, 711, 806, 480, 93, 49, 276, 570, 411, 647, 321, 25, 709, 471, 122, 338] The set of cells that are occupied is {1, 5, 6, 8, 10, 11, 12, 13, 15, 16, 17, 18, 19, 24, 25, 26, 28, 29, 31, 32, 33, 34, 35, 37, 38, 39, 43, 44, 46, 47, 49, 50, 51, 53, 59, 60, 62, 63, 67, 68, 69, 70, 72, 73, 76, 77, 78, 79, 81, 82, 83, 84, 86, 89, 90, 93, 94, 95, 96, 97, 100, 102, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 116, 118, 120, 122, 123, 124, 125, 127, 132, 133, 135, 137, 138, 139, 140, 142, 144, 146, 147, 148, 150, 151, 153, 154, 156, 157, 159, 160, 161, 162, 163, 164, 165, 167, 169, 176, 180, 181, 182, 184, 185, 188, 189, 190, 192, 193, 194, 196, 197, 198, 199, 205, 208, 209, 210, 211, 212, 214, 218, 219, 220, 221, 223, 225, 227, 228, 229, 230, 232, 235, 236, 237, 238, 240, 242, 243, 245, 246, 247, 248, 249, 250, 251, 252, 253, 254, 256, 257, 258, 261, 262, 263, 264, 265, 267, 270, 271, 272, 274, 275, 276, 277, 280, 282, 288, 290, 291, 292, 294, 295, 297, 299, 300, 301, 302, 303, 305, 306, 307, 308, 309, 310, 311, 313, 315, 319, 320, 321, 322, 324, 327, 329, 330, 331, 333, 334, 335, 336, 337, 338, 339, 341, 342, 343, 344, 345, 347, 350, 352, 353, 354, 358, 359, 361, 364, 365, 366, 367, 369, 370, 371, 375, 376, 377, 378, 381, 382, 383, 384, 385, 386, 391, 393, 396, 397, 398, 400, 401, 402, 403, 407, 408, 409, 411, 412, 414, 418, 419, 421, 422, 423, 424, 425, 426, 427, 428, 429, 433, 434, 438, 439, 441, 443, 445, 446, 447, 449, 450, 451, 452, 453, 454, 455, 456, 457, 458, 460, 461, 463, 465, 466, 468, 469, 470, 471, 473, 474, 475, 477, 479, 480, 481, 484, 491, 492, 493, 494, 495, 498, 500, 501, 503, 506, 507, 509, 511, 512, 513, 515, 516, 520, 521, 523, 524, 525, 526, 528, 529, 530, 531, 532, 533, 535, 536, 537, 538, 539, 540, 543, 544, 545, 549, 551, 553, 554, 555, 557, 559, 561, 563, 564, 568, 570, 572, 573, 574, 575, 576, 577, 579, 580, 582, 584, 588, 589, 591, 593, 597, 598, 599, 602, 603, 606, 607, 608, 609, 610, 611, 613, 614, 616, 617, 618, 622, 623, 624, 625, 626, 627, 628, 631, 632, 634, 635, 637, 639, 641, 643, 644, 645, 647, 648, 649, 650, 652, 653, 654, 655, 656, 658, 659, 660, 662, 664, 669, 671, 672, 673, 674, 675, 676, 682, 683, 685, 686, 687, 689, 691, 693, 696, 697, 699, 702, 703, 704, 705, 706, 707, 708, 709, 710, 711, 713, 714, 715, 716, 719, 720, 721, 722, 723, 724, 726, 727, 730, 731, 733, 735, 736, 737, 738, 740, 741, 742, 744, 748, 749, 750, 752, 753, 754, 759, 760, 762, 764, 765, 766, 767, 768, 769, 770, 772, 773, 775, 776, 777, 778, 779, 780, 782, 784, 786, 787, 790, 793, 794, 795, 797, 798, 800, 803, 804, 806, 808, 809, 810, 811, 813, 816, 819, 820, 821, 822, 824, 826, 829, 831, 832, 834, 835, 840, 842, 843, 844, 846, 847, 848, 849, 850, 852, 853, 854, 856, 858, 859, 860, 861, 864, 865, 868, 870, 871, 872, 874, 875, 876, 878, 879, 880, 881, 883, 886, 889, 890, 892, 893, 894, 895, 896, 898, 899, 904, 905, 906, 908, 909, 910, 911, 912, 915, 916, 919, 920, 921, 922, 923, 924, 925, 926, 928, 929, 930, 931, 933, 934, 935, 936, 937, 938, 939, 940, 943, 944, 945, 946, 948, 949, 950, 951, 952, 953, 954, 956, 957, 958, 959, 961, 962, 963, 965, 967, 968, 970, 973, 974, 977, 979, 980, 981, 982, 983, 984, 987, 990, 991, 992, 993, 994, 998, 999, 1000} The set of cells that have exactly one ball in them is {1, 12, 15, 18, 24, 25, 28, 29, 31, 32, 34, 43, 46, 47, 50, 51, 63, 68, 70, 72, 73, 76, 77, 79, 81, 82, 83, 84, 89, 93, 94, 95, 96, 102, 104, 105, 106, 109, 114, 123, 124, 127, 133, 137, 138, 139, 140, 144, 146, 147, 148, 150, 151, 153, 154, 156, 159, 162, 164, 165, 169, 176, 181, 182, 184, 185, 189, 190, 192, 194, 197, 199, 208, 209, 210, 214, 218, 220, 225, 227, 229, 232, 235, 236, 237, 238, 240, 242, 243, 245, 246, 247, 256, 257, 262, 264, 265, 267, 270, 271, 272, 277, 280, 288, 295, 297, 300, 301, 307, 308, 309, 310, 311, 313, 315, 320, 324, 327, 330, 331, 337, 339, 341, 342, 343, 345, 347, 350, 352, 358, 359, 361, 364, 367, 369, 370, 371, 376, 377, 378, 381, 382, 383, 384, 391, 393, 397, 398, 400, 403, 407, 408, 412, 414, 418, 421, 422, 423, 424, 425, 426, 428, 429, 433, 434, 439, 441, 443, 445, 446, 450, 451, 452, 454, 455, 456, 458, 461, 463, 465, 466, 471, 475, 479, 480, 481, 484, 492, 493, 494, 498, 501, 506, 512, 520, 521, 523, 524, 526, 528, 530, 531, 532, 537, 538, 539, 540, 543, 544, 545, 551, 553, 568, 572, 573, 576, 577, 579, 580, 588, 603, 608, 609, 610, 613, 617, 618, 622, 623, 624, 625, 626, 632, 637, 639, 641, 643, 644, 645, 648, 654, 655, 659, 662, 669, 671, 672, 674, 675, 676, 682, 683, 685, 686, 691, 693, 702, 703, 705, 707, 708, 710, 713, 719, 720, 721, 722, 723, 724, 733, 736, 737, 738, 744, 749, 752, 753, 754, 764, 765, 766, 768, 770, 773, 779, 780, 782, 787, 790, 793, 795, 798, 804, 806, 809, 810, 811, 820, 821, 822, 826, 829, 834, 835, 840, 842, 844, 846, 847, 848, 849, 850, 852, 854, 858, 860, 861, 864, 868, 870, 872, 876, 881, 883, 889, 892, 894, 895, 896, 898, 899, 906, 908, 909, 910, 912, 920, 921, 924, 925, 926, 928, 930, 934, 935, 937, 938, 940, 946, 949, 956, 957, 958, 959, 961, 967, 968, 979, 981, 982, 983, 984, 990, 991, 993, 994} We remove these balls and are now left with, 634, balls The, 634, balls landed in the following cells [368, 482, 326, 401, 77, 621, 646, 645, 883, 831, 29, 587, 492, 21, 183, 846, 810, 807, 595, 721, 204, 398, 275, 490, 823, 778, 535, 961, 523, 664, 691, 407, 458, 735, 411, 21, 190, 905, 507, 149, 856, 157, 841, 186, 486, 384, 622, 150, 604, 380, 745, 210, 817, 252, 640, 574, 964, 917, 242, 831, 247, 542, 591, 79, 835, 863, 444, 576, 361, 476, 734, 663, 378, 339, 104, 302, 954, 889, 678, 505, 507, 335, 409, 803, 262, 217, 576, 129, 971, 606, 745, 239, 206, 987, 661, 115, 278, 990, 454, 514, 370, 390, 298, 638, 250, 993, 211, 754, 849, 68, 712, 123, 867, 518, 724, 750, 464, 24, 240, 858, 257, 955, 681, 609, 670, 508, 772, 446, 580, 61, 206, 141, 35, 854, 210, 847, 793, 34, 537, 395, 759, 413, 678, 455, 517, 437, 639, 395, 782, 913, 47, 387, 348, 511, 955, 895, 194, 986, 289, 319, 77, 28, 891, 269, 541, 407, 687, 808, 229, 433, 406, 421, 435, 548, 947, 646, 243, 376, 210, 262, 983, 139, 975, 871, 25, 317, 60, 17, 315, 602, 659, 790, 346, 964, 103, 987, 801, 475, 924, 27, 301, 382, 344, 753, 450, 1, 356, 914, 762, 141, 195, 216, 760, 811, 216, 362, 562, 405, 69, 523, 616, 375, 41, 853, 130, 299, 150, 418, 940, 898, 773, 885, 693, 801, 284, 873, 853, 353, 175, 153, 725, 91, 257, 368, 120, 711, 350, 286, 721, 783, 890, 554, 794, 271, 396, 100, 274, 78, 552, 871, 529, 784, 510, 19, 893, 359, 740, 671, 611, 477, 970, 163, 614, 464, 714, 558, 716, 831, 176, 414, 511, 870, 523, 155, 525, 531, 45, 316, 990, 64, 433, 605, 822, 566, 168, 54, 441, 139, 538, 955, 680, 12, 503, 268, 781, 796, 659, 93, 275, 739, 907, 670, 382, 671, 994, 903, 355, 168, 224, 282, 201, 356, 456, 380, 556, 127, 146, 502, 242, 86, 958, 945, 987, 15, 497, 160, 166, 704, 566, 205, 941, 67, 918, 611, 354, 941, 926, 952, 122, 496, 919, 950, 47, 370, 697, 618, 340, 746, 725, 893, 637, 451, 84, 603, 338, 465, 102, 137, 453, 652, 141, 596, 218, 698, 852, 805, 805, 52, 148, 960, 183, 911, 415, 725, 372, 220, 356, 713, 753, 1000, 281, 738, 207, 689, 938, 38, 815, 646, 645, 318, 430, 401, 107, 57, 893, 537, 255, 62, 859, 870, 465, 178, 225, 255, 969, 709, 658, 525, 658, 933, 705, 63, 81, 903, 283, 930, 197, 733, 725, 713, 891, 251, 432, 142, 851, 714, 736, 168, 997, 472, 505, 585, 537, 107, 991, 460, 506, 569, 800, 261, 260, 819, 390, 719, 184, 943, 173, 821, 913, 533, 110, 874, 325, 644, 86, 163, 805, 100, 10, 464, 935, 630, 330, 24, 727, 626, 829, 478, 31, 467, 330, 198, 264, 292, 854, 643, 679, 810, 442, 517, 389, 692, 555, 956, 748, 687, 237, 619, 929, 370, 946, 768, 466, 569, 317, 597, 875, 886, 640, 926, 425, 876, 360, 975, 299, 357, 901, 244, 401, 883, 228, 518, 41, 372, 530, 937, 867, 680, 912, 626, 601, 699, 492, 856, 674, 988, 927, 242, 910, 343, 105, 673, 761, 108, 427, 472, 596, 905, 145, 739, 196, 556, 45, 996, 394, 82, 471, 530, 411, 307, 844, 991, 827, 773, 391, 687, 856, 460, 226, 985, 964, 928, 75, 892, 488, 295, 331, 560, 436, 57, 38, 64, 917, 547, 120, 984, 564, 947, 706, 716, 503, 424, 41, 687, 292, 931, 842, 65, 907, 557, 845, 27, 813, 385, 959, 527, 517, 138, 345, 441, 563, 530, 825, 199, 234, 699, 807, 105, 319, 216, 219, 271, 210, 668, 250, 274, 498, 302, 468, 45, 483, 972, 667, 645] The set of cells that are occupied is {1, 10, 12, 15, 17, 19, 21, 24, 25, 27, 28, 29, 31, 34, 35, 38, 41, 45, 47, 52, 54, 57, 60, 61, 62, 63, 64, 65, 67, 68, 69, 75, 77, 78, 79, 81, 82, 84, 86, 91, 93, 100, 102, 103, 104, 105, 107, 108, 110, 115, 120, 122, 123, 127, 129, 130, 137, 138, 139, 141, 142, 145, 146, 148, 149, 150, 153, 155, 157, 160, 163, 166, 168, 173, 175, 176, 178, 183, 184, 186, 190, 194, 195, 196, 197, 198, 199, 201, 204, 205, 206, 207, 210, 211, 216, 217, 218, 219, 220, 224, 225, 226, 228, 229, 234, 237, 239, 240, 242, 243, 244, 247, 250, 251, 252, 255, 257, 260, 261, 262, 264, 268, 269, 271, 274, 275, 278, 281, 282, 283, 284, 286, 289, 292, 295, 298, 299, 301, 302, 307, 315, 316, 317, 318, 319, 325, 326, 330, 331, 335, 338, 339, 340, 343, 344, 345, 346, 348, 350, 353, 354, 355, 356, 357, 359, 360, 361, 362, 368, 370, 372, 375, 376, 378, 380, 382, 384, 385, 387, 389, 390, 391, 394, 395, 396, 398, 401, 405, 406, 407, 409, 411, 413, 414, 415, 418, 421, 424, 425, 427, 430, 432, 433, 435, 436, 437, 441, 442, 444, 446, 450, 451, 453, 454, 455, 456, 458, 460, 464, 465, 466, 467, 468, 471, 472, 475, 476, 477, 478, 482, 483, 486, 488, 490, 492, 496, 497, 498, 502, 503, 505, 506, 507, 508, 510, 511, 514, 517, 518, 523, 525, 527, 529, 530, 531, 533, 535, 537, 538, 541, 542, 547, 548, 552, 554, 555, 556, 557, 558, 560, 562, 563, 564, 566, 569, 574, 576, 580, 585, 587, 591, 595, 596, 597, 601, 602, 603, 604, 605, 606, 609, 611, 614, 616, 618, 619, 621, 622, 626, 630, 637, 638, 639, 640, 643, 644, 645, 646, 652, 658, 659, 661, 663, 664, 667, 668, 670, 671, 673, 674, 678, 679, 680, 681, 687, 689, 691, 692, 693, 697, 698, 699, 704, 705, 706, 709, 711, 712, 713, 714, 716, 719, 721, 724, 725, 727, 733, 734, 735, 736, 738, 739, 740, 745, 746, 748, 750, 753, 754, 759, 760, 761, 762, 768, 772, 773, 778, 781, 782, 783, 784, 790, 793, 794, 796, 800, 801, 803, 805, 807, 808, 810, 811, 813, 815, 817, 819, 821, 822, 823, 825, 827, 829, 831, 835, 841, 842, 844, 845, 846, 847, 849, 851, 852, 853, 854, 856, 858, 859, 863, 867, 870, 871, 873, 874, 875, 876, 883, 885, 886, 889, 890, 891, 892, 893, 895, 898, 901, 903, 905, 907, 910, 911, 912, 913, 914, 917, 918, 919, 924, 926, 927, 928, 929, 930, 931, 933, 935, 937, 938, 940, 941, 943, 945, 946, 947, 950, 952, 954, 955, 956, 958, 959, 960, 961, 964, 969, 970, 971, 972, 975, 983, 984, 985, 986, 987, 988, 990, 991, 993, 994, 996, 997, 1000} The set of cells that have exactly one ball in them is {1, 10, 12, 15, 17, 19, 25, 28, 29, 31, 34, 35, 52, 54, 60, 61, 62, 63, 65, 67, 68, 69, 75, 78, 79, 81, 82, 84, 91, 93, 102, 103, 104, 108, 110, 115, 122, 123, 127, 129, 130, 137, 138, 142, 145, 146, 148, 149, 153, 155, 157, 160, 166, 173, 175, 176, 178, 184, 186, 190, 194, 195, 196, 197, 198, 199, 201, 204, 205, 207, 211, 217, 218, 219, 220, 224, 225, 226, 228, 229, 234, 237, 239, 240, 243, 244, 247, 251, 252, 260, 261, 264, 268, 269, 278, 281, 282, 283, 284, 286, 289, 295, 298, 301, 307, 315, 316, 318, 325, 326, 331, 335, 338, 339, 340, 343, 344, 345, 346, 348, 350, 353, 354, 355, 357, 359, 360, 361, 362, 375, 376, 378, 384, 385, 387, 389, 391, 394, 396, 398, 405, 406, 409, 413, 414, 415, 418, 421, 424, 425, 427, 430, 432, 435, 436, 437, 442, 444, 446, 450, 451, 453, 454, 455, 456, 458, 466, 467, 468, 471, 475, 476, 477, 478, 482, 483, 486, 488, 490, 496, 497, 498, 502, 506, 508, 510, 514, 527, 529, 531, 533, 535, 538, 541, 542, 547, 548, 552, 554, 555, 557, 558, 560, 562, 563, 564, 574, 580, 585, 587, 591, 595, 597, 601, 602, 603, 604, 605, 606, 609, 614, 616, 618, 619, 621, 622, 630, 637, 638, 639, 643, 644, 652, 661, 663, 664, 667, 668, 673, 674, 679, 681, 689, 691, 692, 693, 697, 698, 704, 705, 706, 709, 711, 712, 719, 724, 727, 733, 734, 735, 736, 738, 740, 746, 748, 750, 754, 759, 760, 761, 762, 768, 772, 778, 781, 782, 783, 784, 790, 793, 794, 796, 800, 803, 808, 811, 813, 815, 817, 819, 821, 822, 823, 825, 827, 829, 835, 841, 842, 844, 845, 846, 847, 849, 851, 852, 858, 859, 863, 873, 874, 875, 876, 885, 886, 889, 890, 892, 895, 898, 901, 910, 911, 912, 914, 918, 919, 924, 927, 928, 929, 930, 931, 933, 935, 937, 938, 940, 943, 945, 946, 950, 952, 954, 956, 958, 959, 960, 961, 969, 970, 971, 972, 983, 984, 985, 986, 988, 993, 994, 996, 997, 1000} We remove these balls and are now left with, 271, balls The, 271, balls landed in the following cells [49, 583, 559, 28, 206, 35, 601, 251, 27, 798, 92, 644, 594, 993, 141, 639, 74, 564, 716, 782, 940, 766, 561, 23, 374, 341, 57, 418, 919, 612, 517, 346, 90, 788, 406, 66, 138, 675, 374, 198, 406, 482, 184, 11, 727, 4, 841, 122, 112, 137, 680, 351, 690, 448, 93, 337, 349, 755, 899, 823, 222, 91, 473, 167, 968, 477, 57, 203, 724, 216, 251, 742, 315, 237, 438, 473, 270, 799, 951, 744, 232, 553, 274, 234, 665, 239, 34, 509, 396, 552, 273, 99, 39, 330, 294, 806, 265, 396, 618, 364, 510, 942, 491, 446, 462, 782, 273, 837, 297, 609, 373, 119, 42, 672, 1000, 762, 317, 841, 317, 500, 953, 277, 811, 492, 796, 22, 89, 282, 993, 272, 98, 252, 447, 62, 87, 237, 798, 444, 229, 323, 80, 247, 511, 500, 303, 501, 782, 68, 848, 886, 317, 54, 268, 545, 887, 557, 287, 304, 847, 667, 152, 224, 889, 948, 355, 259, 676, 835, 59, 733, 106, 355, 562, 451, 340, 690, 765, 714, 458, 9, 166, 30, 921, 278, 968, 92, 728, 709, 795, 821, 494, 476, 906, 853, 730, 152, 832, 136, 609, 788, 944, 479, 145, 114, 784, 207, 463, 125, 583, 392, 849, 2, 356, 524, 995, 15, 792, 431, 571, 100, 528, 993, 283, 743, 75, 441, 459, 718, 716, 943, 573, 382, 403, 565, 447, 655, 698, 648, 482, 228, 621, 102, 983, 83, 628, 125, 881, 484, 749, 869, 722, 92, 282, 822, 125, 519, 809, 132, 245, 238, 854, 979, 381, 685, 119, 202, 110, 153, 771, 229, 157] The set of cells that are occupied is {2, 4, 9, 11, 15, 22, 23, 27, 28, 30, 34, 35, 39, 42, 49, 54, 57, 59, 62, 66, 68, 74, 75, 80, 83, 87, 89, 90, 91, 92, 93, 98, 99, 100, 102, 106, 110, 112, 114, 119, 122, 125, 132, 136, 137, 138, 141, 145, 152, 153, 157, 166, 167, 184, 198, 202, 203, 206, 207, 216, 222, 224, 228, 229, 232, 234, 237, 238, 239, 245, 247, 251, 252, 259, 265, 268, 270, 272, 273, 274, 277, 278, 282, 283, 287, 294, 297, 303, 304, 315, 317, 323, 330, 337, 340, 341, 346, 349, 351, 355, 356, 364, 373, 374, 381, 382, 392, 396, 403, 406, 418, 431, 438, 441, 444, 446, 447, 448, 451, 458, 459, 462, 463, 473, 476, 477, 479, 482, 484, 491, 492, 494, 500, 501, 509, 510, 511, 517, 519, 524, 528, 545, 552, 553, 557, 559, 561, 562, 564, 565, 571, 573, 583, 594, 601, 609, 612, 618, 621, 628, 639, 644, 648, 655, 665, 667, 672, 675, 676, 680, 685, 690, 698, 709, 714, 716, 718, 722, 724, 727, 728, 730, 733, 742, 743, 744, 749, 755, 762, 765, 766, 771, 782, 784, 788, 792, 795, 796, 798, 799, 806, 809, 811, 821, 822, 823, 832, 835, 837, 841, 847, 848, 849, 853, 854, 869, 881, 886, 887, 889, 899, 906, 919, 921, 940, 942, 943, 944, 948, 951, 953, 968, 979, 983, 993, 995, 1000} The set of cells that have exactly one ball in them is {2, 4, 9, 11, 15, 22, 23, 27, 28, 30, 34, 35, 39, 42, 49, 54, 59, 62, 66, 68, 74, 75, 80, 83, 87, 89, 90, 91, 93, 98, 99, 100, 102, 106, 110, 112, 114, 122, 132, 136, 137, 138, 141, 145, 153, 157, 166, 167, 184, 198, 202, 203, 206, 207, 216, 222, 224, 228, 232, 234, 238, 239, 245, 247, 252, 259, 265, 268, 270, 272, 274, 277, 278, 283, 287, 294, 297, 303, 304, 315, 323, 330, 337, 340, 341, 346, 349, 351, 356, 364, 373, 381, 382, 392, 403, 418, 431, 438, 441, 444, 446, 448, 451, 458, 459, 462, 463, 476, 477, 479, 484, 491, 492, 494, 501, 509, 510, 511, 517, 519, 524, 528, 545, 552, 553, 557, 559, 561, 562, 564, 565, 571, 573, 594, 601, 612, 618, 621, 628, 639, 644, 648, 655, 665, 667, 672, 675, 676, 680, 685, 698, 709, 714, 718, 722, 724, 727, 728, 730, 733, 742, 743, 744, 749, 755, 762, 765, 766, 771, 784, 792, 795, 796, 799, 806, 809, 811, 821, 822, 823, 832, 835, 837, 847, 848, 849, 853, 854, 869, 881, 886, 887, 889, 899, 906, 919, 921, 940, 942, 943, 944, 948, 951, 953, 979, 983, 995, 1000} We remove these balls and are now left with, 63, balls The, 63, balls landed in the following cells [239, 680, 490, 486, 604, 554, 493, 525, 425, 678, 660, 500, 655, 53, 926, 642, 768, 667, 987, 243, 156, 466, 155, 235, 515, 822, 915, 837, 142, 611, 753, 461, 52, 766, 646, 644, 743, 827, 44, 931, 24, 203, 583, 258, 295, 391, 85, 120, 402, 120, 350, 612, 385, 639, 879, 478, 146, 826, 216, 465, 40, 308, 878] The set of cells that are occupied is {24, 40, 44, 52, 53, 85, 120, 142, 146, 155, 156, 203, 216, 235, 239, 243, 258, 295, 308, 350, 385, 391, 402, 425, 461, 465, 466, 478, 486, 490, 493, 500, 515, 525, 554, 583, 604, 611, 612, 639, 642, 644, 646, 655, 660, 667, 678, 680, 743, 753, 766, 768, 822, 826, 827, 837, 878, 879, 915, 926, 931, 987} The set of cells that have exactly one ball in them is {24, 40, 44, 52, 53, 85, 142, 146, 155, 156, 203, 216, 235, 239, 243, 258, 295, 308, 350, 385, 391, 402, 425, 461, 465, 466, 478, 486, 490, 493, 500, 515, 525, 554, 583, 604, 611, 612, 639, 642, 644, 646, 655, 660, 667, 678, 680, 743, 753, 766, 768, 822, 826, 827, 837, 878, 879, 915, 926, 931, 987} We remove these balls and are now left with, 2, balls The, 2, balls landed in the following cells [185, 704] The set of cells that are occupied is {185, 704} The set of cells that have exactly one ball in them is {185, 704} We remove these balls and are now left with, 0, balls This took, 5, rounds The, 1000, balls landed in the following cells [215, 506, 851, 486, 407, 394, 708, 548, 473, 908, 144, 1, 678, 377, 566, 88, 853, 789, 263, 553, 166, 858, 31, 244, 312, 858, 772, 375, 125, 277, 694, 781, 932, 972, 453, 77, 133, 248, 835, 267, 868, 251, 535, 795, 352, 45, 148, 56, 251, 444, 107, 616, 610, 934, 268, 673, 422, 508, 795, 443, 652, 891, 19, 154, 541, 272, 679, 240, 625, 246, 290, 36, 535, 106, 324, 306, 87, 477, 851, 447, 697, 985, 106, 665, 294, 527, 390, 95, 654, 89, 544, 352, 216, 444, 57, 317, 827, 75, 584, 831, 613, 848, 14, 955, 922, 302, 908, 374, 448, 66, 780, 290, 236, 169, 570, 133, 437, 876, 16, 740, 350, 217, 302, 34, 394, 723, 680, 810, 704, 706, 896, 48, 376, 668, 365, 268, 839, 281, 993, 604, 371, 176, 53, 373, 777, 910, 365, 293, 346, 535, 246, 521, 550, 936, 893, 376, 206, 680, 139, 970, 945, 684, 152, 51, 612, 941, 311, 986, 841, 269, 342, 569, 549, 584, 102, 558, 569, 626, 584, 652, 653, 335, 247, 535, 392, 341, 622, 549, 350, 322, 686, 311, 969, 947, 757, 73, 433, 695, 615, 40, 640, 803, 400, 782, 477, 564, 767, 228, 447, 753, 447, 364, 802, 36, 200, 785, 837, 256, 897, 207, 719, 638, 873, 412, 969, 723, 303, 693, 875, 773, 774, 484, 632, 936, 256, 32, 929, 291, 196, 243, 324, 670, 120, 881, 575, 912, 279, 881, 156, 781, 891, 204, 336, 332, 29, 309, 690, 395, 622, 502, 454, 173, 348, 716, 273, 74, 208, 307, 160, 988, 316, 626, 15, 290, 253, 671, 419, 442, 359, 145, 695, 869, 930, 540, 338, 54, 92, 679, 707, 795, 959, 149, 915, 798, 321, 887, 668, 197, 926, 680, 29, 706, 40, 780, 318, 495, 891, 645, 683, 947, 310, 301, 413, 605, 766, 943, 60, 935, 758, 636, 375, 351, 432, 736, 115, 276, 622, 584, 913, 317, 140, 18, 456, 588, 17, 107, 723, 90, 44, 727, 600, 469, 154, 260, 943, 573, 352, 617, 821, 663, 495, 52, 929, 551, 275, 885, 653, 9, 319, 737, 261, 893, 115, 588, 509, 49, 777, 483, 663, 119, 379, 793, 992, 797, 399, 899, 73, 478, 378, 988, 338, 536, 587, 316, 690, 758, 905, 560, 765, 49, 938, 494, 734, 28, 171, 204, 387, 777, 755, 809, 815, 152, 152, 596, 473, 109, 774, 943, 921, 260, 54, 42, 609, 944, 739, 283, 776, 437, 251, 523, 170, 620, 835, 489, 73, 985, 33, 164, 970, 746, 464, 940, 814, 270, 975, 541, 124, 690, 350, 938, 737, 959, 309, 805, 815, 502, 32, 301, 494, 797, 536, 769, 463, 391, 777, 539, 995, 884, 58, 960, 145, 990, 969, 251, 906, 771, 85, 462, 537, 280, 763, 360, 155, 528, 425, 179, 903, 608, 573, 66, 687, 921, 18, 418, 654, 711, 304, 290, 912, 43, 712, 7, 104, 656, 112, 38, 839, 220, 288, 888, 428, 68, 745, 334, 786, 19, 460, 250, 967, 19, 912, 426, 957, 235, 751, 425, 881, 96, 823, 591, 268, 216, 118, 727, 341, 41, 59, 554, 375, 388, 758, 175, 108, 12, 457, 699, 326, 971, 459, 633, 300, 747, 285, 302, 384, 503, 632, 62, 450, 774, 482, 212, 532, 108, 371, 237, 465, 447, 500, 740, 320, 285, 360, 923, 71, 414, 219, 733, 450, 184, 422, 604, 236, 940, 925, 393, 524, 232, 239, 732, 171, 35, 426, 82, 480, 187, 584, 911, 745, 914, 989, 43, 177, 744, 514, 955, 184, 408, 70, 991, 634, 545, 276, 666, 689, 389, 360, 476, 619, 74, 530, 38, 38, 673, 516, 231, 370, 884, 607, 634, 533, 289, 948, 882, 783, 242, 998, 336, 779, 162, 179, 391, 246, 898, 973, 3, 680, 692, 383, 488, 41, 494, 97, 140, 971, 688, 273, 666, 95, 393, 402, 281, 857, 545, 385, 732, 752, 20, 868, 147, 330, 689, 287, 705, 561, 129, 619, 318, 298, 775, 581, 999, 873, 426, 518, 957, 106, 314, 386, 651, 766, 959, 623, 509, 136, 986, 508, 688, 221, 332, 251, 493, 581, 40, 290, 565, 694, 365, 407, 464, 500, 822, 839, 882, 593, 770, 699, 146, 813, 853, 776, 837, 977, 352, 839, 805, 560, 656, 381, 840, 66, 879, 695, 175, 572, 166, 1000, 864, 703, 704, 814, 61, 696, 637, 434, 932, 734, 608, 184, 684, 835, 811, 570, 972, 636, 30, 811, 223, 678, 450, 225, 984, 285, 855, 537, 457, 667, 474, 125, 979, 902, 955, 108, 846, 715, 682, 767, 610, 978, 853, 912, 561, 218, 509, 728, 319, 531, 62, 231, 978, 501, 922, 939, 131, 744, 577, 650, 988, 121, 727, 873, 882, 826, 339, 4, 925, 792, 215, 603, 775, 978, 328, 935, 567, 938, 291, 512, 768, 906, 477, 804, 363, 182, 194, 307, 863, 39, 668, 408, 191, 784, 137, 753, 280, 253, 420, 235, 788, 911, 599, 943, 496, 111, 565, 630, 864, 325, 508, 907, 147, 626, 234, 612, 3, 313, 298, 168, 789, 29, 706, 405, 623, 30, 939, 756, 65, 535, 268, 473, 757, 119, 569, 676, 205, 230, 129, 525, 680, 883, 473, 796, 978, 992, 46, 36, 165, 614, 674, 94, 265, 575, 313, 829, 845, 363, 71, 569, 281, 466, 779, 55, 810, 897, 113, 453, 798, 538, 285, 54, 705, 347, 355, 451, 549, 394, 217, 427, 686, 413, 327, 28, 405, 466, 562, 779, 244, 577, 876, 398, 775, 444, 154, 959, 200, 146, 353, 325, 402, 808, 476, 788, 874, 573, 377, 651, 430, 190, 637, 985, 302, 711, 145, 431, 331, 399, 24, 868, 507, 547, 287, 964, 60, 206, 670, 727, 122, 137, 315, 235, 109, 6, 650, 863, 147, 654, 659, 189, 705, 176, 979, 555, 742, 554, 868, 524, 168, 414, 322, 193, 619, 47, 509, 677, 739, 68, 624, 113, 219, 844, 656, 727, 327, 704, 815, 664, 77, 6, 99, 699, 665] The set of cells that are occupied is {1, 3, 4, 6, 7, 9, 12, 14, 15, 16, 17, 18, 19, 20, 24, 28, 29, 30, 31, 32, 33, 34, 35, 36, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 65, 66, 68, 70, 71, 73, 74, 75, 77, 82, 85, 87, 88, 89, 90, 92, 94, 95, 96, 97, 99, 102, 104, 106, 107, 108, 109, 111, 112, 113, 115, 118, 119, 120, 121, 122, 124, 125, 129, 131, 133, 136, 137, 139, 140, 144, 145, 146, 147, 148, 149, 152, 154, 155, 156, 160, 162, 164, 165, 166, 168, 169, 170, 171, 173, 175, 176, 177, 179, 182, 184, 187, 189, 190, 191, 193, 194, 196, 197, 200, 204, 205, 206, 207, 208, 212, 215, 216, 217, 218, 219, 220, 221, 223, 225, 228, 230, 231, 232, 234, 235, 236, 237, 239, 240, 242, 243, 244, 246, 247, 248, 250, 251, 253, 256, 260, 261, 263, 265, 267, 268, 269, 270, 272, 273, 275, 276, 277, 279, 280, 281, 283, 285, 287, 288, 289, 290, 291, 293, 294, 298, 300, 301, 302, 303, 304, 306, 307, 309, 310, 311, 312, 313, 314, 315, 316, 317, 318, 319, 320, 321, 322, 324, 325, 326, 327, 328, 330, 331, 332, 334, 335, 336, 338, 339, 341, 342, 346, 347, 348, 350, 351, 352, 353, 355, 359, 360, 363, 364, 365, 370, 371, 373, 374, 375, 376, 377, 378, 379, 381, 383, 384, 385, 386, 387, 388, 389, 390, 391, 392, 393, 394, 395, 398, 399, 400, 402, 405, 407, 408, 412, 413, 414, 418, 419, 420, 422, 425, 426, 427, 428, 430, 431, 432, 433, 434, 437, 442, 443, 444, 447, 448, 450, 451, 453, 454, 456, 457, 459, 460, 462, 463, 464, 465, 466, 469, 473, 474, 476, 477, 478, 480, 482, 483, 484, 486, 488, 489, 493, 494, 495, 496, 500, 501, 502, 503, 506, 507, 508, 509, 512, 514, 516, 518, 521, 523, 524, 525, 527, 528, 530, 531, 532, 533, 535, 536, 537, 538, 539, 540, 541, 544, 545, 547, 548, 549, 550, 551, 553, 554, 555, 558, 560, 561, 562, 564, 565, 566, 567, 569, 570, 572, 573, 575, 577, 581, 584, 587, 588, 591, 593, 596, 599, 600, 603, 604, 605, 607, 608, 609, 610, 612, 613, 614, 615, 616, 617, 619, 620, 622, 623, 624, 625, 626, 630, 632, 633, 634, 636, 637, 638, 640, 645, 650, 651, 652, 653, 654, 656, 659, 663, 664, 665, 666, 667, 668, 670, 671, 673, 674, 676, 677, 678, 679, 680, 682, 683, 684, 686, 687, 688, 689, 690, 692, 693, 694, 695, 696, 697, 699, 703, 704, 705, 706, 707, 708, 711, 712, 715, 716, 719, 723, 727, 728, 732, 733, 734, 736, 737, 739, 740, 742, 744, 745, 746, 747, 751, 752, 753, 755, 756, 757, 758, 763, 765, 766, 767, 768, 769, 770, 771, 772, 773, 774, 775, 776, 777, 779, 780, 781, 782, 783, 784, 785, 786, 788, 789, 792, 793, 795, 796, 797, 798, 802, 803, 804, 805, 808, 809, 810, 811, 813, 814, 815, 821, 822, 823, 826, 827, 829, 831, 835, 837, 839, 840, 841, 844, 845, 846, 848, 851, 853, 855, 857, 858, 863, 864, 868, 869, 873, 874, 875, 876, 879, 881, 882, 883, 884, 885, 887, 888, 891, 893, 896, 897, 898, 899, 902, 903, 905, 906, 907, 908, 910, 911, 912, 913, 914, 915, 921, 922, 923, 925, 926, 929, 930, 932, 934, 935, 936, 938, 939, 940, 941, 943, 944, 945, 947, 948, 955, 957, 959, 960, 964, 967, 969, 970, 971, 972, 973, 975, 977, 978, 979, 984, 985, 986, 988, 989, 990, 991, 992, 993, 995, 998, 999, 1000} The set of cells that have exactly one ball in them is {1, 4, 7, 9, 12, 14, 15, 16, 17, 20, 24, 31, 33, 34, 35, 39, 42, 44, 45, 46, 47, 48, 51, 52, 53, 55, 56, 57, 58, 59, 61, 65, 70, 75, 82, 85, 87, 88, 89, 90, 92, 94, 96, 97, 99, 102, 104, 111, 112, 118, 120, 121, 122, 124, 131, 136, 139, 144, 148, 149, 155, 156, 160, 162, 164, 165, 169, 170, 173, 177, 182, 187, 189, 190, 191, 193, 194, 196, 197, 205, 207, 208, 212, 218, 220, 221, 223, 225, 228, 230, 232, 234, 237, 239, 240, 242, 243, 247, 248, 250, 261, 263, 265, 267, 269, 270, 272, 275, 277, 279, 283, 288, 289, 293, 294, 300, 303, 304, 306, 310, 312, 314, 315, 320, 321, 326, 328, 330, 331, 334, 335, 339, 342, 346, 347, 348, 351, 353, 355, 359, 364, 370, 373, 374, 378, 379, 381, 383, 384, 385, 386, 387, 388, 389, 390, 392, 395, 398, 400, 412, 418, 419, 420, 427, 428, 430, 431, 432, 433, 434, 442, 443, 448, 451, 454, 456, 459, 460, 462, 463, 465, 469, 474, 478, 480, 482, 483, 484, 486, 488, 489, 493, 496, 501, 503, 506, 507, 512, 514, 516, 518, 521, 523, 525, 527, 528, 530, 531, 532, 533, 538, 539, 540, 544, 547, 548, 550, 551, 553, 555, 558, 562, 564, 566, 567, 572, 587, 591, 593, 596, 599, 600, 603, 605, 607, 609, 613, 614, 615, 616, 617, 620, 624, 625, 630, 633, 638, 640, 645, 659, 664, 667, 671, 674, 676, 677, 682, 683, 687, 692, 693, 696, 697, 703, 707, 708, 712, 715, 716, 719, 728, 733, 736, 742, 746, 747, 751, 752, 755, 756, 763, 765, 768, 769, 770, 771, 772, 773, 782, 783, 784, 785, 786, 792, 793, 796, 802, 803, 804, 808, 809, 813, 821, 822, 823, 826, 827, 829, 831, 840, 841, 844, 845, 846, 848, 855, 857, 869, 874, 875, 879, 883, 885, 887, 888, 896, 898, 899, 902, 903, 905, 907, 910, 913, 914, 915, 923, 926, 930, 934, 941, 944, 945, 948, 960, 964, 967, 973, 975, 977, 984, 989, 990, 991, 993, 995, 998, 999, 1000} We remove these balls and are now left with, 641, balls The, 641, balls landed in the following cells [36, 163, 186, 552, 470, 353, 190, 20, 490, 599, 177, 293, 97, 985, 454, 622, 524, 172, 757, 100, 654, 940, 186, 659, 746, 527, 909, 195, 542, 403, 133, 691, 317, 500, 777, 765, 316, 506, 890, 374, 798, 151, 838, 333, 920, 231, 226, 171, 271, 760, 846, 659, 422, 496, 39, 139, 924, 464, 475, 373, 560, 364, 799, 341, 906, 236, 373, 254, 753, 276, 783, 688, 767, 320, 551, 738, 171, 628, 820, 755, 420, 981, 512, 332, 105, 149, 419, 468, 184, 385, 780, 452, 468, 552, 780, 658, 273, 854, 686, 537, 627, 736, 290, 10, 102, 806, 521, 971, 526, 214, 282, 222, 993, 85, 708, 182, 191, 536, 600, 567, 377, 288, 28, 757, 229, 335, 385, 868, 603, 667, 278, 238, 72, 7, 663, 635, 616, 311, 551, 333, 279, 336, 450, 637, 421, 376, 65, 654, 929, 229, 316, 963, 511, 405, 930, 177, 564, 728, 649, 443, 959, 922, 430, 874, 183, 698, 147, 637, 651, 872, 860, 800, 438, 355, 113, 606, 159, 753, 492, 285, 246, 396, 159, 820, 902, 851, 828, 58, 493, 648, 843, 983, 613, 197, 98, 447, 726, 419, 413, 285, 926, 770, 886, 57, 872, 204, 74, 312, 502, 45, 249, 621, 480, 272, 269, 416, 473, 269, 825, 245, 658, 715, 853, 805, 471, 806, 463, 667, 562, 96, 899, 112, 152, 281, 172, 35, 386, 821, 831, 450, 745, 925, 106, 49, 351, 293, 871, 960, 345, 793, 605, 63, 147, 654, 402, 684, 796, 782, 54, 62, 741, 3, 368, 545, 661, 891, 588, 795, 549, 557, 763, 544, 663, 647, 368, 936, 132, 375, 13, 416, 220, 999, 44, 606, 919, 913, 601, 649, 82, 52, 81, 585, 598, 316, 660, 361, 29, 158, 235, 457, 333, 855, 138, 785, 939, 838, 512, 629, 542, 852, 187, 126, 571, 129, 94, 679, 330, 226, 508, 761, 222, 560, 347, 682, 769, 953, 592, 826, 463, 563, 352, 852, 786, 77, 130, 456, 660, 151, 948, 546, 416, 683, 670, 576, 914, 64, 684, 40, 438, 943, 481, 676, 410, 342, 156, 883, 233, 307, 883, 355, 921, 91, 947, 911, 738, 809, 962, 47, 831, 883, 503, 499, 42, 161, 300, 479, 430, 33, 256, 972, 839, 33, 70, 728, 433, 356, 535, 98, 453, 94, 50, 687, 751, 114, 816, 464, 401, 716, 523, 17, 978, 784, 942, 3, 619, 351, 301, 603, 163, 580, 762, 633, 50, 710, 152, 241, 949, 599, 766, 876, 608, 778, 908, 571, 411, 322, 833, 156, 398, 528, 766, 328, 9, 1000, 278, 264, 559, 18, 503, 1000, 586, 568, 642, 730, 259, 232, 445, 901, 471, 460, 46, 768, 672, 280, 644, 196, 186, 723, 780, 802, 615, 850, 860, 980, 753, 341, 559, 472, 859, 43, 527, 883, 288, 645, 651, 101, 817, 673, 22, 444, 745, 920, 343, 133, 257, 933, 299, 386, 212, 282, 679, 451, 222, 944, 22, 401, 757, 981, 419, 992, 502, 234, 468, 789, 801, 332, 519, 463, 782, 436, 160, 288, 938, 165, 417, 518, 231, 642, 536, 494, 894, 478, 683, 662, 645, 871, 736, 284, 331, 651, 368, 471, 252, 342, 539, 503, 170, 152, 247, 289, 537, 762, 984, 19, 919, 891, 565, 537, 738, 315, 550, 663, 545, 405, 612, 512, 197, 525, 693, 986, 658, 411, 847, 675, 22, 9, 822, 477, 186, 517, 628, 152, 182, 58, 298, 776, 907, 586, 344, 456, 813, 648, 448, 771, 118, 363, 996, 795, 923, 469, 633, 71, 327, 755, 609, 444, 89, 250, 461, 191, 926, 506, 676, 659, 678, 538, 791, 295, 681, 206, 399, 208, 372, 35, 373, 65, 102, 915, 471, 841, 796, 313, 602, 461, 427, 681, 406, 368, 726, 240, 499, 866, 778, 529, 385, 426, 474, 521, 250, 727, 928] The set of cells that are occupied is {3, 7, 9, 10, 13, 17, 18, 19, 20, 22, 28, 29, 33, 35, 36, 39, 40, 42, 43, 44, 45, 46, 47, 49, 50, 52, 54, 57, 58, 62, 63, 64, 65, 70, 71, 72, 74, 77, 81, 82, 85, 89, 91, 94, 96, 97, 98, 100, 101, 102, 105, 106, 112, 113, 114, 118, 126, 129, 130, 132, 133, 138, 139, 147, 149, 151, 152, 156, 158, 159, 160, 161, 163, 165, 170, 171, 172, 177, 182, 183, 184, 186, 187, 190, 191, 195, 196, 197, 204, 206, 208, 212, 214, 220, 222, 226, 229, 231, 232, 233, 234, 235, 236, 238, 240, 241, 245, 246, 247, 249, 250, 252, 254, 256, 257, 259, 264, 269, 271, 272, 273, 276, 278, 279, 280, 281, 282, 284, 285, 288, 289, 290, 293, 295, 298, 299, 300, 301, 307, 311, 312, 313, 315, 316, 317, 320, 322, 327, 328, 330, 331, 332, 333, 335, 336, 341, 342, 343, 344, 345, 347, 351, 352, 353, 355, 356, 361, 363, 364, 368, 372, 373, 374, 375, 376, 377, 385, 386, 396, 398, 399, 401, 402, 403, 405, 406, 410, 411, 413, 416, 417, 419, 420, 421, 422, 426, 427, 430, 433, 436, 438, 443, 444, 445, 447, 448, 450, 451, 452, 453, 454, 456, 457, 460, 461, 463, 464, 468, 469, 470, 471, 472, 473, 474, 475, 477, 478, 479, 480, 481, 490, 492, 493, 494, 496, 499, 500, 502, 503, 506, 508, 511, 512, 517, 518, 519, 521, 523, 524, 525, 526, 527, 528, 529, 535, 536, 537, 538, 539, 542, 544, 545, 546, 549, 550, 551, 552, 557, 559, 560, 562, 563, 564, 565, 567, 568, 571, 576, 580, 585, 586, 588, 592, 598, 599, 600, 601, 602, 603, 605, 606, 608, 609, 612, 613, 615, 616, 619, 621, 622, 627, 628, 629, 633, 635, 637, 642, 644, 645, 647, 648, 649, 651, 654, 658, 659, 660, 661, 662, 663, 667, 670, 672, 673, 675, 676, 678, 679, 681, 682, 683, 684, 686, 687, 688, 691, 693, 698, 708, 710, 715, 716, 723, 726, 727, 728, 730, 736, 738, 741, 745, 746, 751, 753, 755, 757, 760, 761, 762, 763, 765, 766, 767, 768, 769, 770, 771, 776, 777, 778, 780, 782, 783, 784, 785, 786, 789, 791, 793, 795, 796, 798, 799, 800, 801, 802, 805, 806, 809, 813, 816, 817, 820, 821, 822, 825, 826, 828, 831, 833, 838, 839, 841, 843, 846, 847, 850, 851, 852, 853, 854, 855, 859, 860, 866, 868, 871, 872, 874, 876, 883, 886, 890, 891, 894, 899, 901, 902, 906, 907, 908, 909, 911, 913, 914, 915, 919, 920, 921, 922, 923, 924, 925, 926, 928, 929, 930, 933, 936, 938, 939, 940, 942, 943, 944, 947, 948, 949, 953, 959, 960, 962, 963, 971, 972, 978, 980, 981, 983, 984, 985, 986, 992, 993, 996, 999, 1000} The set of cells that have exactly one ball in them is {7, 10, 13, 17, 18, 19, 20, 28, 29, 36, 39, 40, 42, 43, 44, 45, 46, 47, 49, 52, 54, 57, 62, 63, 64, 70, 71, 72, 74, 77, 81, 82, 85, 89, 91, 96, 97, 100, 101, 105, 106, 112, 113, 114, 118, 126, 129, 130, 132, 138, 139, 149, 158, 160, 161, 165, 170, 183, 184, 187, 190, 195, 196, 204, 206, 208, 212, 214, 220, 232, 233, 234, 235, 236, 238, 240, 241, 245, 246, 247, 249, 252, 254, 256, 257, 259, 264, 271, 272, 273, 276, 279, 280, 281, 284, 289, 290, 295, 298, 299, 300, 301, 307, 311, 312, 313, 315, 317, 320, 322, 327, 328, 330, 331, 335, 336, 343, 344, 345, 347, 352, 353, 356, 361, 363, 364, 372, 374, 375, 376, 377, 396, 398, 399, 402, 403, 406, 410, 413, 417, 420, 421, 422, 426, 427, 433, 436, 443, 445, 447, 448, 451, 452, 453, 454, 457, 460, 469, 470, 472, 473, 474, 475, 477, 478, 479, 480, 481, 490, 492, 493, 494, 496, 500, 508, 511, 517, 518, 519, 523, 524, 525, 526, 528, 529, 535, 538, 539, 544, 546, 549, 550, 557, 562, 563, 564, 565, 567, 568, 576, 580, 585, 588, 592, 598, 600, 601, 602, 605, 608, 609, 612, 613, 615, 616, 619, 621, 622, 627, 629, 635, 644, 647, 661, 662, 670, 672, 673, 675, 678, 682, 686, 687, 688, 691, 693, 698, 708, 710, 715, 716, 723, 727, 730, 741, 746, 751, 760, 761, 763, 765, 767, 768, 769, 770, 771, 776, 777, 783, 784, 785, 786, 789, 791, 793, 798, 799, 800, 801, 802, 805, 809, 813, 816, 817, 821, 822, 825, 826, 828, 833, 839, 841, 843, 846, 847, 850, 851, 853, 854, 855, 859, 866, 868, 874, 876, 886, 890, 894, 899, 901, 902, 906, 907, 908, 909, 911, 913, 914, 915, 921, 922, 923, 924, 925, 928, 929, 930, 933, 936, 938, 939, 940, 942, 943, 944, 947, 948, 949, 953, 959, 960, 962, 963, 971, 972, 978, 980, 983, 984, 985, 986, 992, 993, 996, 999} We remove these balls and are now left with, 295, balls The, 295, balls landed in the following cells [511, 42, 854, 139, 368, 201, 989, 445, 596, 925, 869, 400, 481, 126, 690, 270, 821, 398, 448, 422, 693, 790, 652, 857, 440, 658, 731, 326, 370, 931, 185, 726, 350, 456, 131, 493, 934, 923, 735, 37, 78, 391, 943, 662, 139, 354, 908, 545, 33, 31, 537, 373, 688, 184, 809, 650, 850, 163, 694, 270, 451, 640, 519, 648, 687, 831, 480, 974, 740, 443, 61, 418, 580, 818, 789, 289, 262, 119, 684, 63, 175, 312, 436, 375, 812, 311, 560, 433, 158, 250, 548, 785, 410, 825, 811, 965, 799, 479, 718, 973, 344, 627, 621, 778, 367, 115, 269, 945, 400, 951, 818, 377, 600, 731, 810, 22, 500, 786, 635, 178, 43, 605, 988, 523, 880, 893, 488, 530, 534, 880, 360, 781, 277, 286, 969, 746, 792, 501, 386, 512, 908, 304, 647, 543, 453, 536, 718, 490, 100, 927, 94, 927, 824, 601, 2, 15, 72, 325, 396, 261, 699, 714, 409, 504, 348, 618, 202, 953, 995, 292, 323, 829, 103, 792, 398, 683, 451, 708, 709, 667, 328, 184, 363, 53, 453, 64, 395, 48, 554, 351, 752, 472, 263, 157, 876, 113, 321, 703, 511, 731, 991, 74, 867, 481, 754, 707, 234, 58, 469, 993, 529, 809, 144, 33, 927, 909, 942, 933, 83, 592, 712, 159, 225, 386, 327, 757, 109, 851, 58, 993, 883, 973, 235, 224, 679, 922, 307, 986, 562, 423, 326, 938, 595, 63, 698, 616, 41, 204, 266, 268, 997, 349, 214, 261, 724, 925, 499, 900, 100, 814, 844, 683, 609, 908, 176, 548, 780, 913, 315, 329, 702, 703, 225, 493, 967, 556, 510, 302, 662, 420, 151, 741, 31, 661, 308, 9, 480, 214, 243, 50, 718, 708, 846, 557, 330] The set of cells that are occupied is {2, 9, 15, 22, 31, 33, 37, 41, 42, 43, 48, 50, 53, 58, 61, 63, 64, 72, 74, 78, 83, 94, 100, 103, 109, 113, 115, 119, 126, 131, 139, 144, 151, 157, 158, 159, 163, 175, 176, 178, 184, 185, 201, 202, 204, 214, 224, 225, 234, 235, 243, 250, 261, 262, 263, 266, 268, 269, 270, 277, 286, 289, 292, 302, 304, 307, 308, 311, 312, 315, 321, 323, 325, 326, 327, 328, 329, 330, 344, 348, 349, 350, 351, 354, 360, 363, 367, 368, 370, 373, 375, 377, 386, 391, 395, 396, 398, 400, 409, 410, 418, 420, 422, 423, 433, 436, 440, 443, 445, 448, 451, 453, 456, 469, 472, 479, 480, 481, 488, 490, 493, 499, 500, 501, 504, 510, 511, 512, 519, 523, 529, 530, 534, 536, 537, 543, 545, 548, 554, 556, 557, 560, 562, 580, 592, 595, 596, 600, 601, 605, 609, 616, 618, 621, 627, 635, 640, 647, 648, 650, 652, 658, 661, 662, 667, 679, 683, 684, 687, 688, 690, 693, 694, 698, 699, 702, 703, 707, 708, 709, 712, 714, 718, 724, 726, 731, 735, 740, 741, 746, 752, 754, 757, 778, 780, 781, 785, 786, 789, 790, 792, 799, 809, 810, 811, 812, 814, 818, 821, 824, 825, 829, 831, 844, 846, 850, 851, 854, 857, 867, 869, 876, 880, 883, 893, 900, 908, 909, 913, 922, 923, 925, 927, 931, 933, 934, 938, 942, 943, 945, 951, 953, 965, 967, 969, 973, 974, 986, 988, 989, 991, 993, 995, 997} The set of cells that have exactly one ball in them is {2, 9, 15, 22, 37, 41, 42, 43, 48, 50, 53, 61, 64, 72, 74, 78, 83, 94, 103, 109, 113, 115, 119, 126, 131, 144, 151, 157, 158, 159, 163, 175, 176, 178, 185, 201, 202, 204, 224, 234, 235, 243, 250, 262, 263, 266, 268, 269, 277, 286, 289, 292, 302, 304, 307, 308, 311, 312, 315, 321, 323, 325, 327, 328, 329, 330, 344, 348, 349, 350, 351, 354, 360, 363, 367, 368, 370, 373, 375, 377, 391, 395, 396, 409, 410, 418, 420, 422, 423, 433, 436, 440, 443, 445, 448, 456, 469, 472, 479, 488, 490, 499, 500, 501, 504, 510, 512, 519, 523, 529, 530, 534, 536, 537, 543, 545, 554, 556, 557, 560, 562, 580, 592, 595, 596, 600, 601, 605, 609, 616, 618, 621, 627, 635, 640, 647, 648, 650, 652, 658, 661, 667, 679, 684, 687, 688, 690, 693, 694, 698, 699, 702, 707, 709, 712, 714, 724, 726, 735, 740, 741, 746, 752, 754, 757, 778, 780, 781, 785, 786, 789, 790, 799, 810, 811, 812, 814, 821, 824, 825, 829, 831, 844, 846, 850, 851, 854, 857, 867, 869, 876, 883, 893, 900, 909, 913, 922, 923, 931, 933, 934, 938, 942, 943, 945, 951, 953, 965, 967, 969, 974, 986, 988, 989, 991, 995, 997} We remove these balls and are now left with, 78, balls The, 78, balls landed in the following cells [138, 547, 342, 851, 478, 720, 202, 474, 103, 373, 88, 351, 568, 210, 892, 481, 931, 206, 387, 656, 244, 13, 416, 668, 458, 444, 682, 650, 227, 775, 677, 736, 452, 66, 265, 131, 562, 814, 968, 267, 902, 500, 802, 609, 669, 980, 414, 431, 119, 359, 394, 541, 473, 383, 517, 672, 875, 889, 26, 214, 856, 182, 138, 523, 721, 259, 590, 229, 919, 965, 246, 67, 244, 974, 998, 931, 167, 398] The set of cells that are occupied is {13, 26, 66, 67, 88, 103, 119, 131, 138, 167, 182, 202, 206, 210, 214, 227, 229, 244, 246, 259, 265, 267, 342, 351, 359, 373, 383, 387, 394, 398, 414, 416, 431, 444, 452, 458, 473, 474, 478, 481, 500, 517, 523, 541, 547, 562, 568, 590, 609, 650, 656, 668, 669, 672, 677, 682, 720, 721, 736, 775, 802, 814, 851, 856, 875, 889, 892, 902, 919, 931, 965, 968, 974, 980, 998} The set of cells that have exactly one ball in them is {13, 26, 66, 67, 88, 103, 119, 131, 167, 182, 202, 206, 210, 214, 227, 229, 246, 259, 265, 267, 342, 351, 359, 373, 383, 387, 394, 398, 414, 416, 431, 444, 452, 458, 473, 474, 478, 481, 500, 517, 523, 541, 547, 562, 568, 590, 609, 650, 656, 668, 669, 672, 677, 682, 720, 721, 736, 775, 802, 814, 851, 856, 875, 889, 892, 902, 919, 965, 968, 974, 980, 998} We remove these balls and are now left with, 6, balls The, 6, balls landed in the following cells [945, 446, 166, 221, 252, 181] The set of cells that are occupied is {166, 181, 221, 252, 446, 945} The set of cells that have exactly one ball in them is {166, 181, 221, 252, 446, 945} We remove these balls and are now left with, 0, balls This took, 5, rounds The, 1000, balls landed in the following cells [593, 981, 487, 478, 990, 956, 57, 631, 852, 116, 347, 594, 504, 457, 502, 952, 890, 295, 191, 648, 171, 108, 611, 811, 629, 364, 507, 72, 289, 465, 745, 379, 467, 592, 47, 17, 785, 60, 998, 717, 637, 241, 846, 932, 135, 866, 86, 539, 42, 859, 165, 479, 352, 685, 999, 544, 930, 556, 747, 146, 251, 184, 238, 72, 141, 448, 881, 33, 583, 36, 564, 794, 880, 878, 651, 837, 784, 579, 570, 179, 97, 243, 118, 102, 148, 352, 877, 403, 151, 705, 676, 750, 103, 445, 538, 571, 139, 135, 769, 764, 261, 751, 147, 256, 66, 871, 654, 630, 682, 952, 102, 627, 144, 980, 948, 321, 348, 232, 403, 711, 243, 564, 5, 534, 295, 351, 199, 981, 608, 44, 101, 466, 17, 900, 185, 627, 381, 632, 188, 225, 484, 775, 748, 793, 369, 523, 871, 989, 425, 376, 576, 800, 613, 633, 632, 412, 761, 603, 783, 296, 737, 829, 58, 7, 807, 822, 116, 999, 725, 72, 310, 42, 353, 182, 496, 253, 481, 175, 66, 842, 146, 957, 309, 908, 983, 580, 328, 676, 401, 693, 764, 372, 252, 699, 341, 607, 14, 120, 514, 740, 991, 269, 429, 8, 90, 102, 393, 583, 785, 934, 888, 356, 593, 145, 545, 191, 385, 124, 921, 4, 696, 900, 511, 91, 110, 717, 890, 232, 925, 857, 90, 723, 373, 815, 889, 463, 5, 406, 179, 21, 354, 330, 740, 606, 127, 919, 159, 778, 624, 567, 249, 719, 4, 748, 511, 534, 934, 472, 23, 911, 61, 833, 153, 863, 395, 177, 354, 90, 550, 431, 243, 768, 50, 382, 138, 250, 562, 784, 588, 396, 573, 969, 133, 324, 351, 782, 494, 978, 905, 712, 333, 401, 817, 40, 842, 590, 52, 70, 994, 895, 68, 837, 741, 318, 441, 317, 56, 620, 926, 75, 266, 968, 287, 420, 817, 573, 434, 98, 824, 924, 608, 782, 552, 931, 527, 776, 200, 411, 411, 976, 291, 917, 984, 252, 526, 235, 952, 941, 589, 215, 150, 148, 648, 309, 829, 247, 566, 638, 171, 934, 634, 624, 28, 373, 209, 958, 505, 873, 877, 979, 297, 320, 235, 576, 819, 349, 793, 171, 887, 492, 619, 362, 108, 93, 148, 167, 619, 487, 23, 848, 112, 694, 475, 222, 431, 942, 122, 58, 379, 391, 533, 264, 944, 69, 187, 441, 100, 871, 762, 100, 889, 550, 608, 229, 316, 993, 863, 235, 89, 39, 287, 967, 311, 158, 996, 942, 238, 234, 844, 503, 870, 131, 393, 759, 251, 450, 761, 543, 269, 772, 129, 273, 952, 908, 959, 348, 933, 641, 371, 671, 841, 111, 177, 94, 173, 961, 291, 23, 974, 841, 90, 300, 327, 396, 625, 375, 219, 214, 291, 736, 420, 644, 232, 691, 712, 162, 795, 309, 288, 271, 26, 856, 112, 348, 675, 509, 561, 560, 166, 914, 786, 845, 380, 47, 309, 230, 935, 247, 522, 903, 583, 413, 41, 731, 265, 795, 677, 573, 906, 771, 932, 845, 235, 61, 369, 628, 929, 880, 357, 592, 132, 338, 192, 197, 53, 301, 861, 180, 103, 124, 347, 54, 286, 213, 267, 54, 867, 492, 764, 947, 817, 229, 714, 34, 886, 908, 451, 381, 753, 802, 408, 664, 702, 64, 146, 524, 179, 291, 391, 870, 783, 563, 950, 815, 674, 866, 802, 794, 529, 1000, 340, 533, 473, 250, 710, 456, 936, 191, 255, 746, 484, 913, 813, 291, 898, 876, 881, 652, 614, 605, 638, 635, 230, 822, 736, 730, 879, 952, 247, 266, 890, 379, 873, 796, 263, 805, 688, 26, 860, 316, 501, 518, 207, 323, 694, 742, 485, 629, 178, 768, 438, 184, 276, 925, 769, 707, 521, 284, 441, 388, 911, 278, 900, 640, 575, 901, 111, 663, 163, 10, 951, 354, 576, 99, 966, 525, 658, 893, 612, 356, 391, 725, 590, 470, 336, 802, 559, 327, 662, 598, 302, 584, 644, 954, 71, 643, 750, 486, 403, 442, 248, 404, 109, 710, 198, 93, 901, 222, 691, 92, 616, 30, 1, 987, 708, 558, 697, 392, 546, 868, 494, 803, 92, 327, 848, 251, 302, 174, 787, 600, 897, 723, 997, 922, 386, 130, 257, 972, 611, 914, 125, 178, 735, 434, 466, 213, 534, 714, 201, 718, 817, 444, 315, 377, 552, 310, 550, 112, 605, 203, 935, 704, 722, 821, 510, 63, 37, 774, 225, 225, 92, 592, 900, 41, 902, 688, 386, 906, 142, 350, 179, 941, 862, 60, 399, 335, 42, 248, 614, 11, 16, 443, 749, 19, 693, 445, 521, 771, 37, 258, 371, 142, 575, 585, 408, 331, 669, 341, 837, 293, 840, 318, 839, 503, 626, 130, 217, 104, 488, 836, 133, 570, 672, 16, 213, 740, 25, 568, 240, 360, 960, 508, 332, 878, 44, 131, 608, 726, 189, 510, 248, 177, 931, 87, 111, 133, 685, 222, 756, 839, 736, 28, 762, 763, 402, 10, 871, 890, 798, 373, 183, 560, 963, 733, 104, 954, 677, 906, 310, 583, 773, 45, 195, 259, 946, 678, 267, 866, 36, 397, 909, 312, 74, 156, 199, 539, 725, 323, 425, 284, 88, 826, 245, 524, 413, 278, 337, 886, 867, 122, 665, 870, 736, 814, 242, 202, 302, 154, 853, 909, 637, 283, 404, 221, 982, 187, 862, 272, 496, 100, 577, 182, 949, 401, 784, 27, 736, 944, 148, 969, 272, 608, 353, 767, 984, 970, 658, 793, 644, 931, 802, 935, 785, 823, 279, 602, 24, 436, 657, 384, 207, 605, 633, 962, 435, 145, 558, 297, 210, 16, 864, 160, 546, 626, 423, 55, 642, 589, 302, 92, 904, 443, 930, 727, 477, 378, 220, 41, 879, 674, 691, 936, 864, 531, 357, 976, 920, 424, 992, 647, 712, 283, 383, 933, 843, 267, 107, 522, 263, 63, 290, 136, 694, 323, 167, 26, 496, 890, 845, 562, 462, 808, 616, 875, 657, 653, 996, 501, 103, 29, 388, 874, 500, 1, 304, 77, 118, 858, 6, 829, 992, 368, 833, 670, 829, 447, 181, 866, 552, 426] The set of cells that are occupied is {1, 4, 5, 6, 7, 8, 10, 11, 14, 16, 17, 19, 21, 23, 24, 25, 26, 27, 28, 29, 30, 33, 34, 36, 37, 39, 40, 41, 42, 44, 45, 47, 50, 52, 53, 54, 55, 56, 57, 58, 60, 61, 63, 64, 66, 68, 69, 70, 71, 72, 74, 75, 77, 86, 87, 88, 89, 90, 91, 92, 93, 94, 97, 98, 99, 100, 101, 102, 103, 104, 107, 108, 109, 110, 111, 112, 116, 118, 120, 122, 124, 125, 127, 129, 130, 131, 132, 133, 135, 136, 138, 139, 141, 142, 144, 145, 146, 147, 148, 150, 151, 153, 154, 156, 158, 159, 160, 162, 163, 165, 166, 167, 171, 173, 174, 175, 177, 178, 179, 180, 181, 182, 183, 184, 185, 187, 188, 189, 191, 192, 195, 197, 198, 199, 200, 201, 202, 203, 207, 209, 210, 213, 214, 215, 217, 219, 220, 221, 222, 225, 229, 230, 232, 234, 235, 238, 240, 241, 242, 243, 245, 247, 248, 249, 250, 251, 252, 253, 255, 256, 257, 258, 259, 261, 263, 264, 265, 266, 267, 269, 271, 272, 273, 276, 278, 279, 283, 284, 286, 287, 288, 289, 290, 291, 293, 295, 296, 297, 300, 301, 302, 304, 309, 310, 311, 312, 315, 316, 317, 318, 320, 321, 323, 324, 327, 328, 330, 331, 332, 333, 335, 336, 337, 338, 340, 341, 347, 348, 349, 350, 351, 352, 353, 354, 356, 357, 360, 362, 364, 368, 369, 371, 372, 373, 375, 376, 377, 378, 379, 380, 381, 382, 383, 384, 385, 386, 388, 391, 392, 393, 395, 396, 397, 399, 401, 402, 403, 404, 406, 408, 411, 412, 413, 420, 423, 424, 425, 426, 429, 431, 434, 435, 436, 438, 441, 442, 443, 444, 445, 447, 448, 450, 451, 456, 457, 462, 463, 465, 466, 467, 470, 472, 473, 475, 477, 478, 479, 481, 484, 485, 486, 487, 488, 492, 494, 496, 500, 501, 502, 503, 504, 505, 507, 508, 509, 510, 511, 514, 518, 521, 522, 523, 524, 525, 526, 527, 529, 531, 533, 534, 538, 539, 543, 544, 545, 546, 550, 552, 556, 558, 559, 560, 561, 562, 563, 564, 566, 567, 568, 570, 571, 573, 575, 576, 577, 579, 580, 583, 584, 585, 588, 589, 590, 592, 593, 594, 598, 600, 602, 603, 605, 606, 607, 608, 611, 612, 613, 614, 616, 619, 620, 624, 625, 626, 627, 628, 629, 630, 631, 632, 633, 634, 635, 637, 638, 640, 641, 642, 643, 644, 647, 648, 651, 652, 653, 654, 657, 658, 662, 663, 664, 665, 669, 670, 671, 672, 674, 675, 676, 677, 678, 682, 685, 688, 691, 693, 694, 696, 697, 699, 702, 704, 705, 707, 708, 710, 711, 712, 714, 717, 718, 719, 722, 723, 725, 726, 727, 730, 731, 733, 735, 736, 737, 740, 741, 742, 745, 746, 747, 748, 749, 750, 751, 753, 756, 759, 761, 762, 763, 764, 767, 768, 769, 771, 772, 773, 774, 775, 776, 778, 782, 783, 784, 785, 786, 787, 793, 794, 795, 796, 798, 800, 802, 803, 805, 807, 808, 811, 813, 814, 815, 817, 819, 821, 822, 823, 824, 826, 829, 833, 836, 837, 839, 840, 841, 842, 843, 844, 845, 846, 848, 852, 853, 856, 857, 858, 859, 860, 861, 862, 863, 864, 866, 867, 868, 870, 871, 873, 874, 875, 876, 877, 878, 879, 880, 881, 886, 887, 888, 889, 890, 893, 895, 897, 898, 900, 901, 902, 903, 904, 905, 906, 908, 909, 911, 913, 914, 917, 919, 920, 921, 922, 924, 925, 926, 929, 930, 931, 932, 933, 934, 935, 936, 941, 942, 944, 946, 947, 948, 949, 950, 951, 952, 954, 956, 957, 958, 959, 960, 961, 962, 963, 966, 967, 968, 969, 970, 972, 974, 976, 978, 979, 980, 981, 982, 983, 984, 987, 989, 990, 991, 992, 993, 994, 996, 997, 998, 999, 1000} The set of cells that have exactly one ball in them is {6, 7, 8, 11, 14, 19, 21, 24, 25, 27, 29, 30, 33, 34, 39, 40, 45, 50, 52, 53, 55, 56, 57, 64, 68, 69, 70, 71, 74, 75, 77, 86, 87, 88, 89, 91, 94, 97, 98, 99, 101, 107, 109, 110, 120, 125, 127, 129, 132, 136, 138, 139, 141, 144, 147, 150, 151, 153, 154, 156, 158, 159, 160, 162, 163, 165, 166, 173, 174, 175, 180, 181, 183, 185, 188, 189, 192, 195, 197, 198, 200, 201, 202, 203, 209, 210, 214, 215, 217, 219, 220, 221, 234, 240, 241, 242, 245, 249, 253, 255, 256, 257, 258, 259, 261, 264, 265, 271, 273, 276, 279, 286, 288, 289, 290, 293, 296, 300, 301, 304, 311, 312, 315, 317, 320, 321, 324, 328, 330, 331, 332, 333, 335, 336, 337, 338, 340, 349, 350, 360, 362, 364, 368, 372, 375, 376, 377, 378, 380, 382, 383, 384, 385, 392, 395, 397, 399, 402, 406, 412, 423, 424, 426, 429, 435, 436, 438, 442, 444, 447, 448, 450, 451, 456, 457, 462, 463, 465, 467, 470, 472, 473, 475, 477, 478, 479, 481, 485, 486, 488, 500, 502, 504, 505, 507, 508, 509, 514, 518, 523, 525, 526, 527, 529, 531, 538, 543, 544, 545, 556, 559, 561, 563, 566, 567, 568, 571, 577, 579, 580, 584, 585, 588, 594, 598, 600, 602, 603, 606, 607, 612, 613, 620, 625, 628, 630, 631, 634, 635, 640, 641, 642, 643, 647, 651, 652, 653, 654, 662, 663, 664, 665, 669, 670, 671, 672, 675, 678, 682, 696, 697, 699, 702, 704, 705, 707, 708, 711, 718, 719, 722, 726, 727, 730, 731, 733, 735, 737, 741, 742, 745, 746, 747, 749, 751, 753, 756, 759, 763, 767, 772, 773, 774, 775, 776, 778, 786, 787, 796, 798, 800, 803, 805, 807, 808, 811, 813, 814, 819, 821, 823, 824, 826, 836, 840, 843, 844, 846, 852, 853, 856, 857, 858, 859, 860, 861, 868, 874, 875, 876, 887, 888, 893, 895, 897, 898, 902, 903, 904, 905, 913, 917, 919, 920, 921, 922, 924, 926, 929, 946, 947, 948, 949, 950, 951, 956, 957, 958, 959, 960, 961, 962, 963, 966, 967, 968, 970, 972, 974, 978, 979, 980, 982, 983, 987, 989, 990, 991, 993, 994, 997, 998, 1000} We remove these balls and are now left with, 617, balls The, 617, balls landed in the following cells [112, 284, 883, 138, 517, 592, 656, 929, 760, 839, 176, 899, 115, 105, 878, 30, 99, 943, 116, 350, 179, 951, 454, 197, 508, 295, 385, 620, 507, 453, 845, 896, 283, 239, 450, 883, 184, 162, 847, 457, 2, 19, 375, 9, 527, 432, 865, 462, 477, 69, 765, 166, 91, 845, 592, 281, 748, 180, 76, 367, 540, 524, 311, 40, 645, 392, 207, 58, 330, 97, 460, 930, 834, 435, 161, 255, 421, 13, 923, 688, 197, 850, 275, 40, 445, 945, 86, 709, 423, 493, 433, 851, 164, 200, 687, 985, 394, 224, 5, 573, 498, 594, 723, 669, 936, 318, 881, 364, 968, 283, 834, 499, 853, 776, 328, 555, 909, 255, 390, 854, 172, 301, 136, 272, 593, 246, 321, 993, 956, 232, 486, 716, 777, 412, 280, 715, 77, 863, 651, 101, 454, 649, 724, 26, 869, 801, 488, 45, 190, 195, 309, 581, 846, 737, 465, 831, 417, 105, 246, 262, 796, 13, 194, 254, 797, 959, 744, 152, 539, 925, 22, 146, 695, 21, 843, 422, 380, 691, 650, 564, 303, 542, 395, 212, 54, 913, 98, 181, 76, 459, 73, 691, 741, 524, 290, 459, 879, 259, 217, 336, 663, 269, 319, 102, 706, 170, 429, 506, 953, 377, 218, 151, 350, 1000, 110, 340, 773, 596, 216, 543, 815, 997, 47, 677, 311, 302, 367, 650, 327, 741, 329, 734, 5, 317, 193, 155, 165, 379, 797, 738, 186, 487, 689, 657, 136, 853, 164, 688, 711, 692, 689, 392, 652, 874, 192, 394, 363, 453, 936, 42, 558, 350, 931, 147, 889, 104, 399, 340, 275, 449, 961, 528, 733, 166, 529, 241, 762, 294, 743, 624, 870, 636, 620, 803, 282, 146, 642, 982, 117, 858, 317, 558, 473, 495, 594, 695, 997, 890, 851, 781, 242, 197, 604, 89, 995, 409, 752, 790, 777, 915, 644, 171, 491, 654, 114, 490, 637, 19, 724, 729, 397, 601, 784, 743, 232, 8, 537, 410, 717, 50, 988, 146, 308, 499, 671, 549, 330, 827, 278, 160, 765, 797, 434, 645, 492, 478, 547, 206, 135, 474, 42, 286, 596, 224, 364, 763, 973, 225, 416, 427, 730, 344, 684, 868, 388, 626, 378, 956, 32, 476, 195, 43, 788, 710, 36, 465, 242, 515, 270, 370, 807, 951, 235, 59, 473, 422, 930, 687, 368, 78, 337, 880, 202, 694, 101, 131, 90, 873, 145, 706, 838, 282, 706, 388, 394, 836, 263, 675, 441, 334, 32, 591, 946, 206, 458, 168, 159, 671, 211, 45, 529, 867, 762, 884, 1000, 304, 2, 161, 630, 233, 387, 817, 505, 857, 399, 679, 114, 391, 613, 492, 298, 156, 535, 61, 303, 338, 716, 678, 990, 697, 225, 471, 72, 231, 841, 915, 595, 479, 123, 908, 816, 886, 237, 288, 48, 446, 531, 579, 626, 662, 880, 849, 578, 936, 681, 156, 189, 933, 471, 420, 835, 280, 512, 964, 92, 947, 804, 537, 787, 476, 454, 214, 877, 886, 6, 267, 498, 355, 697, 306, 720, 436, 320, 347, 283, 354, 488, 129, 460, 381, 671, 131, 70, 157, 296, 172, 397, 390, 697, 161, 973, 868, 708, 916, 226, 697, 611, 382, 128, 353, 507, 478, 819, 111, 789, 841, 414, 15, 277, 447, 770, 400, 84, 489, 614, 54, 799, 326, 319, 368, 73, 343, 502, 519, 24, 401, 659, 101, 494, 135, 377, 946, 193, 43, 315, 319, 746, 462, 159, 98, 996, 980, 373, 180, 445, 418, 139, 489, 254, 735, 535, 344, 737, 134, 936, 811, 900, 457, 641, 850, 694, 794, 100, 995, 339, 823, 563, 417, 144, 838, 734, 797, 165, 634, 359, 243, 534, 962, 558, 421, 20, 273, 506, 258, 914, 339, 761] The set of cells that are occupied is {2, 5, 6, 8, 9, 13, 15, 19, 20, 21, 22, 24, 26, 30, 32, 36, 40, 42, 43, 45, 47, 48, 50, 54, 58, 59, 61, 69, 70, 72, 73, 76, 77, 78, 84, 86, 89, 90, 91, 92, 97, 98, 99, 100, 101, 102, 104, 105, 110, 111, 112, 114, 115, 116, 117, 123, 128, 129, 131, 134, 135, 136, 138, 139, 144, 145, 146, 147, 151, 152, 155, 156, 157, 159, 160, 161, 162, 164, 165, 166, 168, 170, 171, 172, 176, 179, 180, 181, 184, 186, 189, 190, 192, 193, 194, 195, 197, 200, 202, 206, 207, 211, 212, 214, 216, 217, 218, 224, 225, 226, 231, 232, 233, 235, 237, 239, 241, 242, 243, 246, 254, 255, 258, 259, 262, 263, 267, 269, 270, 272, 273, 275, 277, 278, 280, 281, 282, 283, 284, 286, 288, 290, 294, 295, 296, 298, 301, 302, 303, 304, 306, 308, 309, 311, 315, 317, 318, 319, 320, 321, 326, 327, 328, 329, 330, 334, 336, 337, 338, 339, 340, 343, 344, 347, 350, 353, 354, 355, 359, 363, 364, 367, 368, 370, 373, 375, 377, 378, 379, 380, 381, 382, 385, 387, 388, 390, 391, 392, 394, 395, 397, 399, 400, 401, 409, 410, 412, 414, 416, 417, 418, 420, 421, 422, 423, 427, 429, 432, 433, 434, 435, 436, 441, 445, 446, 447, 449, 450, 453, 454, 457, 458, 459, 460, 462, 465, 471, 473, 474, 476, 477, 478, 479, 486, 487, 488, 489, 490, 491, 492, 493, 494, 495, 498, 499, 502, 505, 506, 507, 508, 512, 515, 517, 519, 524, 527, 528, 529, 531, 534, 535, 537, 539, 540, 542, 543, 547, 549, 555, 558, 563, 564, 573, 578, 579, 581, 591, 592, 593, 594, 595, 596, 601, 604, 611, 613, 614, 620, 624, 626, 630, 634, 636, 637, 641, 642, 644, 645, 649, 650, 651, 652, 654, 656, 657, 659, 662, 663, 669, 671, 675, 677, 678, 679, 681, 684, 687, 688, 689, 691, 692, 694, 695, 697, 706, 708, 709, 710, 711, 715, 716, 717, 720, 723, 724, 729, 730, 733, 734, 735, 737, 738, 741, 743, 744, 746, 748, 752, 760, 761, 762, 763, 765, 770, 773, 776, 777, 781, 784, 787, 788, 789, 790, 794, 796, 797, 799, 801, 803, 804, 807, 811, 815, 816, 817, 819, 823, 827, 831, 834, 835, 836, 838, 839, 841, 843, 845, 846, 847, 849, 850, 851, 853, 854, 857, 858, 863, 865, 867, 868, 869, 870, 873, 874, 877, 878, 879, 880, 881, 883, 884, 886, 889, 890, 896, 899, 900, 908, 909, 913, 914, 915, 916, 923, 925, 929, 930, 931, 933, 936, 943, 945, 946, 947, 951, 953, 956, 959, 961, 962, 964, 968, 973, 980, 982, 985, 988, 990, 993, 995, 996, 997, 1000} The set of cells that have exactly one ball in them is {6, 8, 9, 15, 20, 21, 22, 24, 26, 30, 36, 47, 48, 50, 58, 59, 61, 69, 70, 72, 77, 78, 84, 86, 89, 90, 91, 92, 97, 99, 100, 102, 104, 110, 111, 112, 115, 116, 117, 123, 128, 129, 134, 138, 139, 144, 145, 147, 151, 152, 155, 157, 160, 162, 168, 170, 171, 176, 179, 181, 184, 186, 189, 190, 192, 194, 200, 202, 207, 211, 212, 214, 216, 217, 218, 226, 231, 233, 235, 237, 239, 241, 243, 258, 259, 262, 263, 267, 269, 270, 272, 273, 277, 278, 281, 284, 286, 288, 290, 294, 295, 296, 298, 301, 302, 304, 306, 308, 309, 315, 318, 320, 321, 326, 327, 328, 329, 334, 336, 337, 338, 343, 347, 353, 354, 355, 359, 363, 370, 373, 375, 378, 379, 380, 381, 382, 385, 387, 391, 395, 400, 401, 409, 410, 412, 414, 416, 418, 420, 423, 427, 429, 432, 433, 434, 435, 436, 441, 446, 447, 449, 450, 458, 474, 477, 479, 486, 487, 490, 491, 493, 494, 495, 502, 505, 508, 512, 515, 517, 519, 527, 528, 531, 534, 539, 540, 542, 543, 547, 549, 555, 563, 564, 573, 578, 579, 581, 591, 593, 595, 601, 604, 611, 613, 614, 624, 630, 634, 636, 637, 641, 642, 644, 649, 651, 652, 654, 656, 657, 659, 662, 663, 669, 675, 677, 678, 679, 681, 684, 692, 708, 709, 710, 711, 715, 717, 720, 723, 729, 730, 733, 735, 738, 744, 746, 748, 752, 760, 761, 763, 770, 773, 776, 781, 784, 787, 788, 789, 790, 794, 796, 799, 801, 803, 804, 807, 811, 815, 816, 817, 819, 823, 827, 831, 835, 836, 839, 843, 846, 847, 849, 854, 857, 858, 863, 865, 867, 869, 870, 873, 874, 877, 878, 879, 881, 884, 889, 890, 896, 899, 900, 908, 909, 913, 914, 916, 923, 925, 929, 931, 933, 943, 945, 947, 953, 959, 961, 962, 964, 968, 980, 982, 985, 988, 990, 993, 996} We remove these balls and are now left with, 290, balls The, 290, balls landed in the following cells [752, 345, 110, 277, 832, 731, 697, 687, 738, 374, 683, 441, 709, 437, 298, 486, 278, 271, 756, 596, 651, 786, 11, 425, 457, 189, 122, 145, 37, 294, 950, 694, 984, 576, 677, 730, 103, 132, 457, 657, 231, 812, 37, 152, 335, 177, 594, 70, 579, 742, 442, 316, 923, 654, 848, 214, 110, 850, 906, 418, 639, 79, 250, 764, 962, 767, 147, 397, 377, 125, 387, 485, 361, 293, 213, 183, 54, 602, 615, 680, 226, 429, 79, 471, 607, 151, 782, 718, 819, 784, 942, 889, 235, 370, 800, 621, 939, 849, 147, 407, 633, 188, 890, 804, 953, 383, 418, 979, 296, 370, 888, 199, 984, 991, 725, 978, 349, 278, 50, 105, 921, 512, 409, 87, 682, 24, 557, 425, 781, 117, 314, 739, 207, 5, 563, 379, 295, 389, 970, 295, 633, 335, 147, 539, 253, 731, 377, 792, 437, 136, 614, 663, 838, 570, 699, 955, 750, 961, 329, 352, 138, 81, 558, 363, 370, 906, 951, 729, 639, 607, 708, 253, 935, 664, 813, 161, 896, 887, 90, 619, 735, 761, 861, 611, 296, 356, 655, 282, 118, 134, 591, 194, 642, 54, 300, 66, 592, 174, 338, 585, 63, 296, 255, 650, 443, 664, 915, 883, 816, 246, 695, 360, 36, 990, 834, 321, 514, 733, 985, 368, 925, 273, 356, 209, 565, 470, 286, 940, 881, 592, 401, 415, 991, 559, 470, 350, 785, 518, 99, 779, 162, 829, 455, 640, 505, 795, 418, 405, 929, 109, 958, 562, 633, 801, 744, 446, 546, 953, 724, 729, 946, 119, 46, 254, 521, 159, 624, 840, 168, 432, 137, 185, 968, 762, 573, 13, 45, 61, 416, 811, 613, 641, 8, 754, 880, 565, 992, 999, 594, 696] The set of cells that are occupied is {5, 8, 11, 13, 24, 36, 37, 45, 46, 50, 54, 61, 63, 66, 70, 79, 81, 87, 90, 99, 103, 105, 109, 110, 117, 118, 119, 122, 125, 132, 134, 136, 137, 138, 145, 147, 151, 152, 159, 161, 162, 168, 174, 177, 183, 185, 188, 189, 194, 199, 207, 209, 213, 214, 226, 231, 235, 246, 250, 253, 254, 255, 271, 273, 277, 278, 282, 286, 293, 294, 295, 296, 298, 300, 314, 316, 321, 329, 335, 338, 345, 349, 350, 352, 356, 360, 361, 363, 368, 370, 374, 377, 379, 383, 387, 389, 397, 401, 405, 407, 409, 415, 416, 418, 425, 429, 432, 437, 441, 442, 443, 446, 455, 457, 470, 471, 485, 486, 505, 512, 514, 518, 521, 539, 546, 557, 558, 559, 562, 563, 565, 570, 573, 576, 579, 585, 591, 592, 594, 596, 602, 607, 611, 613, 614, 615, 619, 621, 624, 633, 639, 640, 641, 642, 650, 651, 654, 655, 657, 663, 664, 677, 680, 682, 683, 687, 694, 695, 696, 697, 699, 708, 709, 718, 724, 725, 729, 730, 731, 733, 735, 738, 739, 742, 744, 750, 752, 754, 756, 761, 762, 764, 767, 779, 781, 782, 784, 785, 786, 792, 795, 800, 801, 804, 811, 812, 813, 816, 819, 829, 832, 834, 838, 840, 848, 849, 850, 861, 880, 881, 883, 887, 888, 889, 890, 896, 906, 915, 921, 923, 925, 929, 935, 939, 940, 942, 946, 950, 951, 953, 955, 958, 961, 962, 968, 970, 978, 979, 984, 985, 990, 991, 992, 999} The set of cells that have exactly one ball in them is {5, 8, 11, 13, 24, 36, 45, 46, 50, 61, 63, 66, 70, 81, 87, 90, 99, 103, 105, 109, 117, 118, 119, 122, 125, 132, 134, 136, 137, 138, 145, 151, 152, 159, 161, 162, 168, 174, 177, 183, 185, 188, 189, 194, 199, 207, 209, 213, 214, 226, 231, 235, 246, 250, 254, 255, 271, 273, 277, 282, 286, 293, 294, 298, 300, 314, 316, 321, 329, 338, 345, 349, 350, 352, 360, 361, 363, 368, 374, 379, 383, 387, 389, 397, 401, 405, 407, 409, 415, 416, 429, 432, 441, 442, 443, 446, 455, 471, 485, 486, 505, 512, 514, 518, 521, 539, 546, 557, 558, 559, 562, 563, 570, 573, 576, 579, 585, 591, 596, 602, 611, 613, 614, 615, 619, 621, 624, 640, 641, 642, 650, 651, 654, 655, 657, 663, 677, 680, 682, 683, 687, 694, 695, 696, 697, 699, 708, 709, 718, 724, 725, 730, 733, 735, 738, 739, 742, 744, 750, 752, 754, 756, 761, 762, 764, 767, 779, 781, 782, 784, 785, 786, 792, 795, 800, 801, 804, 811, 812, 813, 816, 819, 829, 832, 834, 838, 840, 848, 849, 850, 861, 880, 881, 883, 887, 888, 889, 890, 896, 915, 921, 923, 925, 929, 935, 939, 940, 942, 946, 950, 951, 955, 958, 961, 962, 968, 970, 978, 979, 985, 990, 992, 999} We remove these balls and are now left with, 67, balls The, 67, balls landed in the following cells [837, 286, 821, 527, 609, 650, 696, 781, 75, 385, 564, 695, 538, 494, 360, 408, 416, 795, 844, 153, 126, 359, 947, 753, 77, 3, 367, 349, 514, 758, 816, 189, 263, 393, 564, 695, 341, 602, 721, 770, 488, 552, 403, 505, 74, 929, 507, 487, 102, 94, 913, 627, 616, 888, 984, 495, 118, 736, 971, 409, 844, 502, 616, 974, 52, 336, 5] The set of cells that are occupied is {3, 5, 52, 74, 75, 77, 94, 102, 118, 126, 153, 189, 263, 286, 336, 341, 349, 359, 360, 367, 385, 393, 403, 408, 409, 416, 487, 488, 494, 495, 502, 505, 507, 514, 527, 538, 552, 564, 602, 609, 616, 627, 650, 695, 696, 721, 736, 753, 758, 770, 781, 795, 816, 821, 837, 844, 888, 913, 929, 947, 971, 974, 984} The set of cells that have exactly one ball in them is {3, 5, 52, 74, 75, 77, 94, 102, 118, 126, 153, 189, 263, 286, 336, 341, 349, 359, 360, 367, 385, 393, 403, 408, 409, 416, 487, 488, 494, 495, 502, 505, 507, 514, 527, 538, 552, 602, 609, 627, 650, 696, 721, 736, 753, 758, 770, 781, 795, 816, 821, 837, 888, 913, 929, 947, 971, 974, 984} We remove these balls and are now left with, 8, balls The, 8, balls landed in the following cells [466, 819, 843, 899, 201, 451, 111, 288] The set of cells that are occupied is {111, 201, 288, 451, 466, 819, 843, 899} The set of cells that have exactly one ball in them is {111, 201, 288, 451, 466, 819, 843, 899} We remove these balls and are now left with, 0, balls This took, 5, rounds The, 1000, balls landed in the following cells [633, 867, 45, 639, 27, 769, 746, 928, 42, 838, 974, 561, 318, 240, 895, 839, 385, 403, 456, 623, 640, 765, 367, 897, 903, 119, 426, 961, 405, 25, 29, 684, 921, 266, 383, 972, 23, 857, 263, 314, 174, 553, 366, 280, 216, 256, 949, 539, 380, 622, 461, 358, 14, 243, 4, 535, 841, 504, 486, 599, 567, 903, 506, 150, 415, 574, 709, 498, 266, 389, 766, 289, 317, 915, 462, 637, 71, 795, 243, 397, 238, 947, 273, 514, 62, 585, 506, 799, 542, 193, 220, 986, 950, 526, 662, 315, 883, 377, 579, 723, 500, 684, 476, 71, 853, 541, 796, 762, 644, 736, 838, 247, 751, 806, 614, 944, 120, 611, 602, 997, 399, 693, 115, 463, 347, 843, 372, 708, 898, 114, 312, 554, 988, 494, 145, 265, 952, 98, 644, 673, 371, 632, 25, 947, 463, 972, 346, 201, 50, 417, 563, 8, 408, 642, 889, 538, 423, 509, 969, 729, 354, 322, 720, 455, 882, 714, 120, 532, 149, 557, 705, 121, 243, 631, 761, 761, 929, 414, 732, 120, 991, 511, 607, 599, 90, 579, 126, 837, 978, 595, 957, 580, 190, 816, 506, 343, 60, 687, 550, 981, 543, 531, 211, 317, 535, 820, 47, 266, 279, 292, 17, 100, 379, 915, 933, 335, 546, 658, 613, 888, 146, 62, 259, 917, 82, 186, 589, 891, 26, 294, 401, 395, 286, 350, 677, 874, 754, 906, 491, 791, 204, 182, 590, 741, 82, 178, 347, 78, 319, 386, 762, 508, 66, 211, 8, 897, 601, 599, 835, 442, 194, 285, 308, 819, 132, 225, 917, 70, 596, 909, 296, 705, 143, 727, 86, 76, 705, 699, 454, 657, 818, 328, 147, 774, 847, 570, 75, 927, 242, 944, 524, 169, 973, 966, 634, 928, 979, 651, 145, 286, 229, 706, 182, 935, 107, 575, 296, 947, 561, 445, 906, 949, 938, 603, 26, 818, 8, 407, 139, 113, 477, 768, 623, 223, 166, 896, 808, 859, 907, 441, 505, 344, 926, 907, 588, 102, 533, 42, 975, 308, 654, 728, 656, 716, 72, 193, 675, 506, 943, 959, 282, 550, 394, 428, 669, 969, 956, 601, 608, 259, 148, 959, 62, 545, 964, 788, 844, 197, 18, 615, 212, 169, 177, 596, 609, 186, 387, 624, 556, 915, 249, 139, 501, 395, 196, 328, 132, 185, 628, 391, 255, 212, 52, 181, 230, 796, 111, 711, 391, 667, 133, 762, 841, 555, 489, 458, 654, 739, 764, 629, 486, 582, 518, 400, 400, 542, 688, 306, 408, 245, 82, 519, 389, 703, 720, 350, 923, 78, 940, 629, 143, 885, 45, 736, 427, 267, 643, 726, 781, 476, 3, 788, 489, 936, 69, 817, 275, 592, 362, 760, 787, 386, 931, 454, 752, 503, 377, 845, 224, 48, 813, 577, 176, 56, 205, 439, 5, 492, 347, 436, 716, 994, 335, 935, 502, 483, 301, 306, 668, 763, 141, 376, 539, 98, 389, 992, 324, 127, 431, 229, 732, 904, 457, 432, 554, 937, 142, 1000, 862, 647, 491, 185, 683, 746, 573, 492, 780, 948, 101, 813, 110, 372, 526, 340, 214, 927, 139, 426, 254, 144, 851, 412, 17, 127, 135, 860, 907, 523, 387, 63, 546, 804, 470, 541, 847, 738, 212, 616, 170, 8, 701, 311, 592, 545, 612, 201, 318, 198, 477, 720, 426, 614, 680, 850, 767, 557, 71, 171, 464, 649, 692, 208, 377, 660, 185, 69, 222, 379, 767, 96, 724, 722, 672, 520, 561, 986, 521, 531, 87, 281, 414, 79, 196, 156, 299, 535, 695, 518, 785, 170, 980, 388, 615, 243, 59, 845, 42, 372, 223, 838, 675, 548, 1000, 355, 376, 266, 510, 325, 38, 738, 268, 63, 775, 871, 543, 548, 274, 552, 862, 507, 250, 876, 598, 661, 181, 114, 771, 140, 82, 192, 42, 223, 164, 283, 88, 609, 760, 943, 163, 710, 479, 186, 280, 535, 93, 389, 595, 963, 745, 735, 156, 696, 203, 267, 492, 882, 272, 411, 169, 594, 435, 165, 155, 837, 709, 418, 171, 883, 697, 230, 311, 478, 679, 557, 594, 13, 487, 25, 569, 871, 844, 56, 31, 188, 149, 318, 223, 352, 212, 707, 889, 639, 432, 932, 674, 614, 253, 830, 501, 361, 836, 886, 800, 955, 964, 271, 831, 755, 309, 997, 29, 67, 780, 468, 549, 14, 88, 8, 36, 170, 379, 538, 767, 69, 820, 895, 482, 360, 276, 334, 1, 188, 725, 706, 219, 757, 795, 13, 20, 803, 289, 175, 708, 829, 494, 757, 188, 802, 646, 887, 106, 969, 333, 73, 464, 775, 44, 67, 933, 329, 368, 461, 201, 731, 822, 792, 841, 792, 778, 574, 378, 884, 225, 880, 950, 758, 9, 23, 698, 315, 848, 42, 500, 235, 412, 165, 766, 234, 276, 924, 899, 866, 223, 442, 233, 514, 22, 644, 736, 27, 37, 171, 436, 112, 248, 269, 444, 753, 818, 466, 15, 124, 720, 474, 873, 401, 843, 487, 981, 331, 806, 988, 800, 17, 926, 119, 58, 141, 989, 941, 935, 38, 821, 171, 700, 703, 443, 316, 611, 641, 751, 136, 167, 316, 444, 69, 634, 201, 460, 173, 169, 872, 824, 363, 832, 928, 103, 440, 853, 339, 323, 700, 303, 786, 709, 884, 755, 99, 311, 920, 563, 5, 147, 234, 782, 765, 750, 787, 102, 154, 443, 866, 591, 477, 92, 390, 49, 564, 399, 822, 939, 85, 90, 873, 646, 338, 38, 90, 343, 725, 183, 63, 661, 569, 96, 442, 810, 440, 587, 265, 993, 287, 898, 195, 556, 842, 981, 442, 569, 582, 610, 798, 308, 759, 259, 464, 797, 931, 874, 201, 239, 715, 355, 263, 964, 308, 956, 211, 768, 317, 431, 507, 282, 377, 334, 628, 665, 72, 474, 661, 901, 725, 83, 32, 978, 164, 471, 801, 355, 390, 99, 453, 968, 722, 308, 914, 588, 199, 503, 667, 407, 615, 499, 56, 760, 3, 549, 356, 643, 213, 842, 408, 316, 426, 882, 559, 871, 987, 584, 994, 953, 18, 815, 150, 432, 599, 298, 78, 184, 461] The set of cells that are occupied is {1, 3, 4, 5, 8, 9, 13, 14, 15, 17, 18, 20, 22, 23, 25, 26, 27, 29, 31, 32, 36, 37, 38, 42, 44, 45, 47, 48, 49, 50, 52, 56, 58, 59, 60, 62, 63, 66, 67, 69, 70, 71, 72, 73, 75, 76, 78, 79, 82, 83, 85, 86, 87, 88, 90, 92, 93, 96, 98, 99, 100, 101, 102, 103, 106, 107, 110, 111, 112, 113, 114, 115, 119, 120, 121, 124, 126, 127, 132, 133, 135, 136, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 154, 155, 156, 163, 164, 165, 166, 167, 169, 170, 171, 173, 174, 175, 176, 177, 178, 181, 182, 183, 184, 185, 186, 188, 190, 192, 193, 194, 195, 196, 197, 198, 199, 201, 203, 204, 205, 208, 211, 212, 213, 214, 216, 219, 220, 222, 223, 224, 225, 229, 230, 233, 234, 235, 238, 239, 240, 242, 243, 245, 247, 248, 249, 250, 253, 254, 255, 256, 259, 263, 265, 266, 267, 268, 269, 271, 272, 273, 274, 275, 276, 279, 280, 281, 282, 283, 285, 286, 287, 289, 292, 294, 296, 298, 299, 301, 303, 306, 308, 309, 311, 312, 314, 315, 316, 317, 318, 319, 322, 323, 324, 325, 328, 329, 331, 333, 334, 335, 338, 339, 340, 343, 344, 346, 347, 350, 352, 354, 355, 356, 358, 360, 361, 362, 363, 366, 367, 368, 371, 372, 376, 377, 378, 379, 380, 383, 385, 386, 387, 388, 389, 390, 391, 394, 395, 397, 399, 400, 401, 403, 405, 407, 408, 411, 412, 414, 415, 417, 418, 423, 426, 427, 428, 431, 432, 435, 436, 439, 440, 441, 442, 443, 444, 445, 453, 454, 455, 456, 457, 458, 460, 461, 462, 463, 464, 466, 468, 470, 471, 474, 476, 477, 478, 479, 482, 483, 486, 487, 489, 491, 492, 494, 498, 499, 500, 501, 502, 503, 504, 505, 506, 507, 508, 509, 510, 511, 514, 518, 519, 520, 521, 523, 524, 526, 531, 532, 533, 535, 538, 539, 541, 542, 543, 545, 546, 548, 549, 550, 552, 553, 554, 555, 556, 557, 559, 561, 563, 564, 567, 569, 570, 573, 574, 575, 577, 579, 580, 582, 584, 585, 587, 588, 589, 590, 591, 592, 594, 595, 596, 598, 599, 601, 602, 603, 607, 608, 609, 610, 611, 612, 613, 614, 615, 616, 622, 623, 624, 628, 629, 631, 632, 633, 634, 637, 639, 640, 641, 642, 643, 644, 646, 647, 649, 651, 654, 656, 657, 658, 660, 661, 662, 665, 667, 668, 669, 672, 673, 674, 675, 677, 679, 680, 683, 684, 687, 688, 692, 693, 695, 696, 697, 698, 699, 700, 701, 703, 705, 706, 707, 708, 709, 710, 711, 714, 715, 716, 720, 722, 723, 724, 725, 726, 727, 728, 729, 731, 732, 735, 736, 738, 739, 741, 745, 746, 750, 751, 752, 753, 754, 755, 757, 758, 759, 760, 761, 762, 763, 764, 765, 766, 767, 768, 769, 771, 774, 775, 778, 780, 781, 782, 785, 786, 787, 788, 791, 792, 795, 796, 797, 798, 799, 800, 801, 802, 803, 804, 806, 808, 810, 813, 815, 816, 817, 818, 819, 820, 821, 822, 824, 829, 830, 831, 832, 835, 836, 837, 838, 839, 841, 842, 843, 844, 845, 847, 848, 850, 851, 853, 857, 859, 860, 862, 866, 867, 871, 872, 873, 874, 876, 880, 882, 883, 884, 885, 886, 887, 888, 889, 891, 895, 896, 897, 898, 899, 901, 903, 904, 906, 907, 909, 914, 915, 917, 920, 921, 923, 924, 926, 927, 928, 929, 931, 932, 933, 935, 936, 937, 938, 939, 940, 941, 943, 944, 947, 948, 949, 950, 952, 953, 955, 956, 957, 959, 961, 963, 964, 966, 968, 969, 972, 973, 974, 975, 978, 979, 980, 981, 986, 987, 988, 989, 991, 992, 993, 994, 997, 1000} The set of cells that have exactly one ball in them is {1, 4, 9, 15, 20, 22, 31, 32, 36, 37, 44, 47, 48, 49, 50, 52, 58, 59, 60, 66, 70, 73, 75, 76, 79, 83, 85, 86, 87, 92, 93, 100, 101, 103, 106, 107, 110, 111, 112, 113, 115, 121, 124, 126, 133, 135, 136, 140, 142, 144, 146, 148, 154, 155, 163, 166, 167, 173, 174, 175, 176, 177, 178, 183, 184, 190, 192, 194, 195, 197, 198, 199, 203, 204, 205, 208, 213, 214, 216, 219, 220, 222, 224, 233, 235, 238, 239, 240, 242, 245, 247, 248, 249, 250, 253, 254, 255, 256, 268, 269, 271, 272, 273, 274, 275, 279, 281, 283, 285, 287, 292, 294, 298, 299, 301, 303, 309, 312, 314, 319, 322, 323, 324, 325, 329, 331, 333, 338, 339, 340, 344, 346, 352, 354, 356, 358, 360, 361, 362, 363, 366, 367, 368, 371, 378, 380, 383, 385, 388, 394, 397, 403, 405, 411, 415, 417, 418, 423, 427, 428, 435, 439, 441, 445, 453, 455, 456, 457, 458, 460, 462, 466, 468, 470, 471, 478, 479, 482, 483, 498, 499, 502, 504, 505, 508, 509, 510, 511, 519, 520, 521, 523, 524, 532, 533, 552, 553, 555, 559, 564, 567, 570, 573, 575, 577, 580, 584, 585, 587, 589, 590, 591, 598, 602, 603, 607, 608, 610, 612, 613, 616, 622, 624, 631, 632, 633, 637, 640, 641, 642, 647, 649, 651, 656, 657, 658, 660, 662, 665, 668, 669, 672, 673, 674, 677, 679, 680, 683, 687, 688, 692, 693, 695, 696, 697, 698, 699, 701, 707, 710, 711, 714, 715, 723, 724, 726, 727, 728, 729, 731, 735, 739, 741, 745, 750, 752, 753, 754, 758, 759, 763, 764, 769, 771, 774, 778, 781, 782, 785, 786, 791, 797, 798, 799, 801, 802, 803, 804, 808, 810, 815, 816, 817, 819, 821, 824, 829, 830, 831, 832, 835, 836, 839, 848, 850, 851, 857, 859, 860, 867, 872, 876, 880, 885, 886, 887, 888, 891, 896, 899, 901, 904, 909, 914, 920, 921, 923, 924, 929, 932, 936, 937, 938, 939, 940, 941, 948, 952, 953, 955, 957, 961, 963, 966, 968, 973, 974, 975, 979, 980, 987, 989, 991, 992, 993} We remove these balls and are now left with, 635, balls The, 635, balls landed in the following cells [253, 633, 26, 610, 738, 135, 7, 915, 231, 219, 27, 244, 582, 362, 347, 381, 252, 309, 745, 690, 895, 557, 236, 86, 501, 461, 424, 838, 700, 409, 991, 385, 546, 724, 347, 6, 470, 288, 188, 754, 381, 836, 846, 278, 415, 457, 548, 430, 161, 726, 800, 631, 537, 922, 567, 600, 458, 186, 728, 445, 769, 205, 754, 534, 322, 917, 747, 415, 327, 455, 599, 606, 543, 17, 368, 265, 148, 202, 706, 436, 504, 824, 234, 651, 743, 693, 520, 474, 880, 677, 526, 91, 203, 823, 761, 366, 731, 801, 697, 975, 572, 949, 753, 949, 405, 809, 246, 930, 324, 975, 508, 687, 413, 91, 957, 866, 649, 221, 758, 744, 467, 519, 990, 787, 447, 241, 818, 789, 434, 143, 490, 416, 846, 550, 134, 477, 677, 910, 868, 243, 871, 444, 74, 461, 158, 112, 257, 591, 569, 408, 252, 704, 925, 219, 140, 465, 94, 824, 947, 683, 57, 184, 43, 388, 320, 13, 511, 7, 971, 171, 994, 283, 602, 544, 288, 155, 926, 705, 995, 313, 138, 267, 753, 247, 292, 481, 818, 536, 327, 100, 404, 866, 530, 346, 249, 441, 100, 381, 42, 696, 740, 308, 936, 568, 403, 415, 76, 386, 179, 451, 421, 112, 550, 901, 941, 594, 454, 797, 263, 496, 750, 505, 144, 370, 229, 631, 29, 687, 763, 904, 516, 249, 204, 701, 272, 126, 727, 607, 901, 480, 990, 990, 400, 908, 761, 741, 899, 33, 899, 429, 624, 618, 768, 117, 305, 389, 381, 879, 676, 244, 519, 83, 869, 748, 832, 90, 945, 610, 646, 567, 469, 23, 314, 302, 929, 677, 317, 778, 970, 979, 890, 21, 684, 273, 298, 549, 800, 12, 826, 897, 827, 8, 310, 961, 127, 630, 972, 777, 879, 858, 938, 315, 567, 784, 354, 935, 197, 855, 355, 308, 288, 900, 242, 46, 577, 143, 453, 364, 499, 949, 123, 71, 984, 117, 247, 706, 260, 417, 222, 568, 22, 501, 437, 463, 980, 783, 186, 403, 647, 639, 552, 806, 913, 425, 814, 632, 939, 799, 782, 613, 668, 526, 14, 208, 518, 732, 729, 746, 767, 752, 255, 69, 33, 103, 422, 729, 769, 272, 273, 118, 507, 912, 624, 675, 683, 134, 444, 302, 163, 975, 611, 595, 151, 418, 912, 113, 906, 350, 427, 886, 844, 358, 674, 688, 359, 491, 262, 954, 379, 367, 224, 601, 321, 947, 89, 97, 240, 367, 774, 455, 934, 685, 594, 996, 464, 54, 850, 838, 286, 464, 750, 869, 782, 663, 1000, 776, 399, 898, 726, 927, 110, 174, 952, 64, 564, 842, 897, 947, 876, 28, 71, 228, 652, 225, 163, 873, 719, 10, 318, 210, 748, 603, 67, 542, 128, 695, 707, 958, 634, 85, 564, 137, 621, 384, 736, 298, 87, 17, 851, 338, 645, 63, 568, 720, 813, 825, 865, 771, 435, 692, 423, 472, 553, 23, 327, 955, 143, 614, 278, 421, 34, 129, 675, 138, 936, 223, 3, 89, 708, 685, 554, 500, 194, 709, 660, 7, 427, 93, 615, 503, 811, 870, 856, 654, 380, 375, 566, 808, 780, 65, 670, 852, 795, 358, 685, 245, 843, 274, 589, 653, 426, 555, 833, 758, 350, 932, 286, 800, 475, 740, 659, 412, 448, 195, 291, 557, 527, 695, 448, 373, 869, 171, 484, 248, 403, 283, 520, 483, 506, 721, 61, 989, 145, 385, 85, 394, 863, 713, 665, 429, 154, 404, 227, 491, 420, 903, 3, 637, 638, 336, 984, 542, 227, 272, 242, 283, 683, 293, 551, 259, 522, 287, 498, 215, 650, 992, 456, 414, 604, 207, 278, 592, 81, 684, 307, 487, 568, 711, 936, 523, 750, 524, 449, 740, 654, 164, 943, 381, 535, 795, 183, 217, 896, 155, 84, 473, 345, 47, 334, 273, 60, 692, 136, 474, 694] The set of cells that are occupied is {3, 6, 7, 8, 10, 12, 13, 14, 17, 21, 22, 23, 26, 27, 28, 29, 33, 34, 42, 43, 46, 47, 54, 57, 60, 61, 63, 64, 65, 67, 69, 71, 74, 76, 81, 83, 84, 85, 86, 87, 89, 90, 91, 93, 94, 97, 100, 103, 110, 112, 113, 117, 118, 123, 126, 127, 128, 129, 134, 135, 136, 137, 138, 140, 143, 144, 145, 148, 151, 154, 155, 158, 161, 163, 164, 171, 174, 179, 183, 184, 186, 188, 194, 195, 197, 202, 203, 204, 205, 207, 208, 210, 215, 217, 219, 221, 222, 223, 224, 225, 227, 228, 229, 231, 234, 236, 240, 241, 242, 243, 244, 245, 246, 247, 248, 249, 252, 253, 255, 257, 259, 260, 262, 263, 265, 267, 272, 273, 274, 278, 283, 286, 287, 288, 291, 292, 293, 298, 302, 305, 307, 308, 309, 310, 313, 314, 315, 317, 318, 320, 321, 322, 324, 327, 334, 336, 338, 345, 346, 347, 350, 354, 355, 358, 359, 362, 364, 366, 367, 368, 370, 373, 375, 379, 380, 381, 384, 385, 386, 388, 389, 394, 399, 400, 403, 404, 405, 408, 409, 412, 413, 414, 415, 416, 417, 418, 420, 421, 422, 423, 424, 425, 426, 427, 429, 430, 434, 435, 436, 437, 441, 444, 445, 447, 448, 449, 451, 453, 454, 455, 456, 457, 458, 461, 463, 464, 465, 467, 469, 470, 472, 473, 474, 475, 477, 480, 481, 483, 484, 487, 490, 491, 496, 498, 499, 500, 501, 503, 504, 505, 506, 507, 508, 511, 516, 518, 519, 520, 522, 523, 524, 526, 527, 530, 534, 535, 536, 537, 542, 543, 544, 546, 548, 549, 550, 551, 552, 553, 554, 555, 557, 564, 566, 567, 568, 569, 572, 577, 582, 589, 591, 592, 594, 595, 599, 600, 601, 602, 603, 604, 606, 607, 610, 611, 613, 614, 615, 618, 621, 624, 630, 631, 632, 633, 634, 637, 638, 639, 645, 646, 647, 649, 650, 651, 652, 653, 654, 659, 660, 663, 665, 668, 670, 674, 675, 676, 677, 683, 684, 685, 687, 688, 690, 692, 693, 694, 695, 696, 697, 700, 701, 704, 705, 706, 707, 708, 709, 711, 713, 719, 720, 721, 724, 726, 727, 728, 729, 731, 732, 736, 738, 740, 741, 743, 744, 745, 746, 747, 748, 750, 752, 753, 754, 758, 761, 763, 767, 768, 769, 771, 774, 776, 777, 778, 780, 782, 783, 784, 787, 789, 795, 797, 799, 800, 801, 806, 808, 809, 811, 813, 814, 818, 823, 824, 825, 826, 827, 832, 833, 836, 838, 842, 843, 844, 846, 850, 851, 852, 855, 856, 858, 863, 865, 866, 868, 869, 870, 871, 873, 876, 879, 880, 886, 890, 895, 896, 897, 898, 899, 900, 901, 903, 904, 906, 908, 910, 912, 913, 915, 917, 922, 925, 926, 927, 929, 930, 932, 934, 935, 936, 938, 939, 941, 943, 945, 947, 949, 952, 954, 955, 957, 958, 961, 970, 971, 972, 975, 979, 980, 984, 989, 990, 991, 992, 994, 995, 996, 1000} The set of cells that have exactly one ball in them is {6, 8, 10, 12, 13, 14, 21, 22, 26, 27, 28, 29, 34, 42, 43, 46, 47, 54, 57, 60, 61, 63, 64, 65, 67, 69, 74, 76, 81, 83, 84, 86, 87, 90, 93, 94, 97, 103, 110, 113, 118, 123, 126, 127, 128, 129, 135, 136, 137, 140, 144, 145, 148, 151, 154, 158, 161, 164, 174, 179, 183, 184, 188, 194, 195, 197, 202, 203, 204, 205, 207, 208, 210, 215, 217, 221, 222, 223, 224, 225, 228, 229, 231, 234, 236, 240, 241, 243, 245, 246, 248, 253, 255, 257, 259, 260, 262, 263, 265, 267, 274, 287, 291, 292, 293, 305, 307, 309, 310, 313, 314, 315, 317, 318, 320, 321, 322, 324, 334, 336, 338, 345, 346, 354, 355, 359, 362, 364, 366, 368, 370, 373, 375, 379, 380, 384, 386, 388, 389, 394, 399, 400, 405, 408, 409, 412, 413, 414, 416, 417, 418, 420, 422, 423, 424, 425, 426, 430, 434, 435, 436, 437, 441, 445, 447, 449, 451, 453, 454, 456, 457, 458, 463, 465, 467, 469, 470, 472, 473, 475, 477, 480, 481, 483, 484, 487, 490, 496, 498, 499, 500, 503, 504, 505, 506, 507, 508, 511, 516, 518, 522, 523, 524, 527, 530, 534, 535, 536, 537, 543, 544, 546, 548, 549, 551, 552, 553, 554, 555, 566, 569, 572, 577, 582, 589, 591, 592, 595, 599, 600, 601, 602, 603, 604, 606, 607, 611, 613, 614, 615, 618, 621, 630, 632, 633, 634, 637, 638, 639, 645, 646, 647, 649, 650, 651, 652, 653, 659, 660, 663, 665, 668, 670, 674, 676, 688, 690, 693, 694, 696, 697, 700, 701, 704, 705, 707, 708, 709, 711, 713, 719, 720, 721, 724, 727, 728, 731, 732, 736, 738, 741, 743, 744, 745, 746, 747, 752, 763, 767, 768, 771, 774, 776, 777, 778, 780, 783, 784, 787, 789, 797, 799, 801, 806, 808, 809, 811, 813, 814, 823, 825, 826, 827, 832, 833, 836, 842, 843, 844, 850, 851, 852, 855, 856, 858, 863, 865, 868, 870, 871, 873, 876, 880, 886, 890, 895, 896, 898, 900, 903, 904, 906, 908, 910, 913, 915, 917, 922, 925, 926, 927, 929, 930, 932, 934, 935, 938, 939, 941, 943, 945, 952, 954, 955, 957, 958, 961, 970, 971, 972, 979, 980, 989, 991, 992, 994, 995, 996, 1000} We remove these balls and are now left with, 246, balls The, 246, balls landed in the following cells [89, 765, 896, 96, 337, 4, 249, 510, 495, 235, 165, 960, 176, 555, 711, 233, 999, 492, 103, 416, 986, 940, 104, 759, 194, 579, 633, 723, 263, 604, 172, 489, 747, 727, 261, 684, 696, 243, 134, 560, 938, 777, 217, 622, 907, 865, 951, 583, 695, 496, 403, 495, 917, 864, 873, 224, 129, 282, 629, 616, 551, 620, 416, 929, 261, 551, 611, 156, 998, 542, 152, 300, 193, 959, 542, 220, 562, 169, 546, 426, 899, 74, 944, 96, 820, 412, 48, 256, 574, 231, 367, 724, 243, 647, 61, 578, 874, 974, 881, 246, 936, 594, 669, 104, 722, 61, 847, 166, 636, 775, 987, 830, 600, 882, 77, 162, 450, 803, 138, 327, 322, 344, 859, 451, 114, 902, 560, 890, 107, 903, 628, 406, 389, 309, 556, 180, 678, 834, 560, 862, 604, 827, 792, 732, 962, 417, 270, 747, 516, 719, 44, 836, 318, 873, 462, 909, 326, 723, 707, 292, 495, 331, 710, 128, 902, 595, 439, 523, 365, 416, 276, 592, 65, 67, 257, 409, 935, 338, 451, 517, 509, 120, 59, 149, 962, 513, 925, 128, 744, 270, 884, 353, 18, 469, 788, 926, 827, 220, 10, 609, 760, 831, 283, 386, 51, 407, 987, 52, 342, 108, 866, 571, 280, 50, 632, 658, 869, 500, 570, 131, 383, 908, 469, 541, 218, 557, 698, 963, 657, 753, 139, 155, 1, 908, 182, 343, 637, 168, 325, 545, 558, 587, 618, 290, 451, 733] The set of cells that are occupied is {1, 4, 10, 18, 44, 48, 50, 51, 52, 59, 61, 65, 67, 74, 77, 89, 96, 103, 104, 107, 108, 114, 120, 128, 129, 131, 134, 138, 139, 149, 152, 155, 156, 162, 165, 166, 168, 169, 172, 176, 180, 182, 193, 194, 217, 218, 220, 224, 231, 233, 235, 243, 246, 249, 256, 257, 261, 263, 270, 276, 280, 282, 283, 290, 292, 300, 309, 318, 322, 325, 326, 327, 331, 337, 338, 342, 343, 344, 353, 365, 367, 383, 386, 389, 403, 406, 407, 409, 412, 416, 417, 426, 439, 450, 451, 462, 469, 489, 492, 495, 496, 500, 509, 510, 513, 516, 517, 523, 541, 542, 545, 546, 551, 555, 556, 557, 558, 560, 562, 570, 571, 574, 578, 579, 583, 587, 592, 594, 595, 600, 604, 609, 611, 616, 618, 620, 622, 628, 629, 632, 633, 636, 637, 647, 657, 658, 669, 678, 684, 695, 696, 698, 707, 710, 711, 719, 722, 723, 724, 727, 732, 733, 744, 747, 753, 759, 760, 765, 775, 777, 788, 792, 803, 820, 827, 830, 831, 834, 836, 847, 859, 862, 864, 865, 866, 869, 873, 874, 881, 882, 884, 890, 896, 899, 902, 903, 907, 908, 909, 917, 925, 926, 929, 935, 936, 938, 940, 944, 951, 959, 960, 962, 963, 974, 986, 987, 998, 999} The set of cells that have exactly one ball in them is {1, 4, 10, 18, 44, 48, 50, 51, 52, 59, 65, 67, 74, 77, 89, 103, 107, 108, 114, 120, 129, 131, 134, 138, 139, 149, 152, 155, 156, 162, 165, 166, 168, 169, 172, 176, 180, 182, 193, 194, 217, 218, 224, 231, 233, 235, 246, 249, 256, 257, 263, 276, 280, 282, 283, 290, 292, 300, 309, 318, 322, 325, 326, 327, 331, 337, 338, 342, 343, 344, 353, 365, 367, 383, 386, 389, 403, 406, 407, 409, 412, 417, 426, 439, 450, 462, 489, 492, 496, 500, 509, 510, 513, 516, 517, 523, 541, 545, 546, 555, 556, 557, 558, 562, 570, 571, 574, 578, 579, 583, 587, 592, 594, 595, 600, 609, 611, 616, 618, 620, 622, 628, 629, 632, 633, 636, 637, 647, 657, 658, 669, 678, 684, 695, 696, 698, 707, 710, 711, 719, 722, 724, 727, 732, 733, 744, 753, 759, 760, 765, 775, 777, 788, 792, 803, 820, 830, 831, 834, 836, 847, 859, 862, 864, 865, 866, 869, 874, 881, 882, 884, 890, 896, 899, 903, 907, 909, 917, 925, 926, 929, 935, 936, 938, 940, 944, 951, 959, 960, 963, 974, 986, 998, 999} We remove these balls and are now left with, 52, balls The, 52, balls landed in the following cells [209, 579, 178, 573, 345, 560, 272, 23, 486, 981, 162, 277, 172, 289, 832, 719, 539, 780, 264, 191, 75, 316, 740, 842, 647, 304, 204, 514, 501, 381, 554, 960, 128, 472, 634, 832, 515, 102, 734, 719, 868, 50, 635, 224, 763, 920, 109, 633, 528, 146, 600, 307] The set of cells that are occupied is {23, 50, 75, 102, 109, 128, 146, 162, 172, 178, 191, 204, 209, 224, 264, 272, 277, 289, 304, 307, 316, 345, 381, 472, 486, 501, 514, 515, 528, 539, 554, 560, 573, 579, 600, 633, 634, 635, 647, 719, 734, 740, 763, 780, 832, 842, 868, 920, 960, 981} The set of cells that have exactly one ball in them is {23, 50, 75, 102, 109, 128, 146, 162, 172, 178, 191, 204, 209, 224, 264, 272, 277, 289, 304, 307, 316, 345, 381, 472, 486, 501, 514, 515, 528, 539, 554, 560, 573, 579, 600, 633, 634, 635, 647, 734, 740, 763, 780, 842, 868, 920, 960, 981} We remove these balls and are now left with, 4, balls The, 4, balls landed in the following cells [617, 143, 488, 935] The set of cells that are occupied is {143, 488, 617, 935} The set of cells that have exactly one ball in them is {143, 488, 617, 935} We remove these balls and are now left with, 0, balls This took, 5, rounds The, 1000, balls landed in the following cells [976, 131, 204, 569, 571, 79, 676, 140, 429, 970, 947, 736, 734, 127, 958, 179, 662, 429, 566, 917, 785, 979, 706, 404, 500, 317, 598, 791, 148, 969, 758, 886, 764, 902, 766, 717, 672, 839, 852, 222, 693, 513, 433, 566, 549, 934, 697, 63, 515, 638, 105, 332, 69, 328, 623, 634, 875, 611, 377, 508, 14, 160, 115, 967, 655, 131, 439, 551, 251, 279, 919, 108, 394, 527, 649, 750, 560, 142, 725, 290, 687, 262, 266, 603, 870, 512, 407, 605, 782, 774, 795, 23, 765, 663, 955, 160, 925, 552, 869, 599, 294, 216, 789, 998, 662, 845, 18, 227, 724, 776, 485, 901, 796, 405, 388, 216, 749, 63, 639, 720, 7, 511, 802, 467, 933, 44, 967, 683, 94, 519, 525, 876, 30, 191, 344, 889, 999, 136, 946, 359, 744, 458, 842, 15, 312, 759, 176, 291, 784, 499, 105, 318, 505, 585, 779, 91, 883, 509, 464, 447, 70, 714, 201, 284, 790, 657, 567, 478, 713, 688, 975, 30, 357, 174, 300, 325, 109, 871, 970, 448, 755, 221, 155, 535, 649, 615, 649, 199, 455, 632, 36, 269, 173, 214, 229, 985, 661, 233, 881, 724, 106, 309, 875, 312, 435, 191, 700, 892, 202, 445, 737, 356, 260, 403, 519, 834, 768, 443, 932, 761, 675, 372, 795, 949, 696, 985, 419, 230, 586, 270, 251, 128, 920, 90, 664, 237, 248, 210, 937, 659, 279, 354, 82, 832, 43, 328, 506, 264, 879, 296, 821, 706, 744, 486, 805, 97, 808, 529, 14, 860, 442, 946, 666, 95, 858, 392, 562, 645, 612, 728, 320, 316, 432, 207, 69, 992, 788, 963, 912, 911, 375, 407, 989, 735, 698, 339, 20, 115, 140, 379, 252, 91, 204, 775, 904, 159, 950, 384, 748, 589, 569, 445, 748, 799, 630, 291, 585, 58, 338, 475, 674, 235, 609, 834, 8, 936, 112, 546, 397, 834, 698, 88, 491, 701, 607, 676, 251, 993, 308, 856, 711, 524, 865, 437, 575, 103, 764, 331, 855, 263, 373, 733, 571, 931, 530, 623, 840, 144, 315, 652, 692, 651, 141, 667, 683, 450, 119, 34, 165, 878, 373, 866, 60, 563, 305, 829, 606, 808, 787, 140, 503, 202, 257, 224, 36, 744, 403, 17, 136, 246, 101, 439, 967, 562, 726, 779, 1000, 767, 712, 334, 457, 383, 767, 995, 8, 167, 942, 704, 748, 563, 304, 202, 39, 851, 522, 40, 320, 615, 125, 508, 877, 274, 407, 500, 888, 22, 118, 803, 513, 381, 407, 807, 603, 936, 903, 676, 419, 633, 655, 64, 670, 364, 415, 305, 605, 479, 510, 623, 82, 921, 110, 473, 413, 974, 247, 488, 416, 817, 299, 7, 959, 543, 480, 327, 484, 728, 470, 189, 243, 795, 553, 707, 736, 782, 457, 655, 720, 468, 941, 87, 568, 77, 258, 481, 196, 316, 947, 92, 920, 381, 292, 508, 789, 935, 565, 514, 143, 695, 525, 319, 348, 617, 18, 403, 615, 989, 884, 127, 764, 467, 558, 663, 18, 792, 508, 609, 967, 45, 433, 474, 972, 505, 796, 597, 68, 286, 572, 413, 877, 68, 3, 44, 661, 462, 315, 125, 769, 588, 682, 298, 550, 263, 568, 984, 537, 859, 186, 464, 763, 335, 77, 591, 380, 748, 107, 359, 526, 811, 240, 706, 673, 29, 397, 144, 374, 389, 865, 721, 340, 301, 876, 940, 116, 329, 304, 642, 658, 479, 189, 342, 742, 359, 225, 156, 847, 423, 257, 66, 238, 705, 945, 762, 193, 469, 237, 835, 825, 176, 602, 736, 638, 913, 279, 184, 527, 47, 571, 927, 235, 780, 623, 990, 582, 567, 247, 177, 146, 74, 196, 855, 103, 559, 265, 526, 603, 830, 577, 657, 241, 323, 806, 646, 308, 563, 768, 589, 126, 984, 91, 791, 967, 206, 521, 577, 858, 402, 90, 847, 544, 288, 338, 395, 533, 478, 353, 789, 423, 312, 440, 393, 97, 617, 163, 671, 912, 207, 782, 546, 623, 581, 232, 998, 210, 541, 748, 923, 829, 721, 792, 532, 55, 451, 934, 921, 36, 640, 348, 627, 713, 975, 176, 333, 549, 143, 402, 174, 88, 563, 725, 363, 941, 541, 616, 280, 895, 203, 481, 901, 481, 61, 535, 236, 151, 836, 384, 144, 90, 628, 862, 29, 730, 523, 675, 931, 638, 235, 461, 215, 951, 269, 238, 318, 551, 259, 79, 774, 258, 100, 876, 238, 89, 856, 832, 867, 638, 951, 740, 432, 69, 898, 779, 293, 222, 853, 720, 67, 63, 922, 421, 710, 375, 853, 416, 679, 178, 609, 641, 59, 487, 603, 346, 258, 624, 356, 579, 627, 261, 127, 956, 166, 245, 911, 488, 960, 24, 376, 595, 205, 830, 528, 874, 779, 377, 614, 429, 658, 910, 912, 623, 962, 154, 187, 906, 651, 769, 690, 200, 167, 216, 498, 636, 2, 359, 895, 307, 253, 909, 705, 459, 801, 337, 882, 267, 302, 610, 750, 626, 881, 483, 483, 246, 724, 875, 899, 306, 135, 849, 982, 467, 363, 986, 9, 254, 211, 188, 417, 738, 244, 201, 442, 962, 893, 83, 654, 774, 97, 906, 418, 751, 701, 832, 223, 679, 757, 213, 197, 517, 588, 58, 922, 524, 999, 562, 464, 665, 676, 274, 925, 936, 51, 140, 524, 794, 391, 100, 628, 496, 72, 681, 775, 436, 651, 711, 480, 532, 15, 316, 394, 515, 30, 261, 822, 950, 758, 657, 62, 767, 310, 734, 823, 615, 983, 974, 493, 408, 605, 295, 531, 949, 240, 887, 42, 972, 786, 373, 227, 995, 675, 79, 718, 461, 728, 763, 62, 928, 477, 763, 565, 905, 249, 615, 796, 696, 819, 876, 493, 924, 448, 411, 806, 969, 189, 419, 659, 874, 620, 270, 163, 217, 772, 724, 48, 886, 562, 861, 505, 150, 895, 87, 370, 811, 263, 972, 403, 590, 635, 460, 162, 32, 668, 416, 640, 677, 276, 909, 501, 405, 81, 558, 571, 334, 333, 579, 473, 25, 951, 419, 474, 913, 664, 167, 392, 704, 549, 517, 845, 928, 151, 899, 759] The set of cells that are occupied is {2, 3, 7, 8, 9, 14, 15, 17, 18, 20, 22, 23, 24, 25, 29, 30, 32, 34, 36, 39, 40, 42, 43, 44, 45, 47, 48, 51, 55, 58, 59, 60, 61, 62, 63, 64, 66, 67, 68, 69, 70, 72, 74, 77, 79, 81, 82, 83, 87, 88, 89, 90, 91, 92, 94, 95, 97, 100, 101, 103, 105, 106, 107, 108, 109, 110, 112, 115, 116, 118, 119, 125, 126, 127, 128, 131, 135, 136, 140, 141, 142, 143, 144, 146, 148, 150, 151, 154, 155, 156, 159, 160, 162, 163, 165, 166, 167, 173, 174, 176, 177, 178, 179, 184, 186, 187, 188, 189, 191, 193, 196, 197, 199, 200, 201, 202, 203, 204, 205, 206, 207, 210, 211, 213, 214, 215, 216, 217, 221, 222, 223, 224, 225, 227, 229, 230, 232, 233, 235, 236, 237, 238, 240, 241, 243, 244, 245, 246, 247, 248, 249, 251, 252, 253, 254, 257, 258, 259, 260, 261, 262, 263, 264, 265, 266, 267, 269, 270, 274, 276, 279, 280, 284, 286, 288, 290, 291, 292, 293, 294, 295, 296, 298, 299, 300, 301, 302, 304, 305, 306, 307, 308, 309, 310, 312, 315, 316, 317, 318, 319, 320, 323, 325, 327, 328, 329, 331, 332, 333, 334, 335, 337, 338, 339, 340, 342, 344, 346, 348, 353, 354, 356, 357, 359, 363, 364, 370, 372, 373, 374, 375, 376, 377, 379, 380, 381, 383, 384, 388, 389, 391, 392, 393, 394, 395, 397, 402, 403, 404, 405, 407, 408, 411, 413, 415, 416, 417, 418, 419, 421, 423, 429, 432, 433, 435, 436, 437, 439, 440, 442, 443, 445, 447, 448, 450, 451, 455, 457, 458, 459, 460, 461, 462, 464, 467, 468, 469, 470, 473, 474, 475, 477, 478, 479, 480, 481, 483, 484, 485, 486, 487, 488, 491, 493, 496, 498, 499, 500, 501, 503, 505, 506, 508, 509, 510, 511, 512, 513, 514, 515, 517, 519, 521, 522, 523, 524, 525, 526, 527, 528, 529, 530, 531, 532, 533, 535, 537, 541, 543, 544, 546, 549, 550, 551, 552, 553, 558, 559, 560, 562, 563, 565, 566, 567, 568, 569, 571, 572, 575, 577, 579, 581, 582, 585, 586, 588, 589, 590, 591, 595, 597, 598, 599, 602, 603, 605, 606, 607, 609, 610, 611, 612, 614, 615, 616, 617, 620, 623, 624, 626, 627, 628, 630, 632, 633, 634, 635, 636, 638, 639, 640, 641, 642, 645, 646, 649, 651, 652, 654, 655, 657, 658, 659, 661, 662, 663, 664, 665, 666, 667, 668, 670, 671, 672, 673, 674, 675, 676, 677, 679, 681, 682, 683, 687, 688, 690, 692, 693, 695, 696, 697, 698, 700, 701, 704, 705, 706, 707, 710, 711, 712, 713, 714, 717, 718, 720, 721, 724, 725, 726, 728, 730, 733, 734, 735, 736, 737, 738, 740, 742, 744, 748, 749, 750, 751, 755, 757, 758, 759, 761, 762, 763, 764, 765, 766, 767, 768, 769, 772, 774, 775, 776, 779, 780, 782, 784, 785, 786, 787, 788, 789, 790, 791, 792, 794, 795, 796, 799, 801, 802, 803, 805, 806, 807, 808, 811, 817, 819, 821, 822, 823, 825, 829, 830, 832, 834, 835, 836, 839, 840, 842, 845, 847, 849, 851, 852, 853, 855, 856, 858, 859, 860, 861, 862, 865, 866, 867, 869, 870, 871, 874, 875, 876, 877, 878, 879, 881, 882, 883, 884, 886, 887, 888, 889, 892, 893, 895, 898, 899, 901, 902, 903, 904, 905, 906, 909, 910, 911, 912, 913, 917, 919, 920, 921, 922, 923, 924, 925, 927, 928, 931, 932, 933, 934, 935, 936, 937, 940, 941, 942, 945, 946, 947, 949, 950, 951, 955, 956, 958, 959, 960, 962, 963, 967, 969, 970, 972, 974, 975, 976, 979, 982, 983, 984, 985, 986, 989, 990, 992, 993, 995, 998, 999, 1000} The set of cells that have exactly one ball in them is {2, 3, 9, 17, 20, 22, 23, 24, 25, 32, 34, 39, 40, 42, 43, 45, 47, 48, 51, 55, 59, 60, 61, 64, 66, 67, 70, 72, 74, 81, 83, 89, 92, 94, 95, 101, 106, 107, 108, 109, 110, 112, 116, 118, 119, 126, 128, 135, 141, 142, 146, 148, 150, 154, 155, 156, 159, 162, 165, 166, 173, 177, 178, 179, 184, 186, 187, 188, 193, 197, 199, 200, 203, 205, 206, 211, 213, 214, 215, 217, 221, 223, 224, 225, 229, 230, 232, 233, 236, 241, 243, 244, 245, 248, 249, 252, 253, 254, 259, 260, 262, 264, 265, 266, 267, 276, 280, 284, 286, 288, 290, 292, 293, 294, 295, 296, 298, 299, 300, 301, 302, 306, 307, 309, 310, 317, 319, 323, 325, 327, 329, 331, 332, 335, 337, 339, 340, 342, 344, 346, 353, 354, 357, 364, 370, 372, 374, 376, 379, 380, 383, 388, 389, 391, 393, 395, 404, 408, 411, 415, 417, 418, 421, 435, 436, 437, 440, 443, 447, 450, 451, 455, 458, 459, 460, 462, 468, 469, 470, 475, 477, 484, 485, 486, 487, 491, 496, 498, 499, 501, 503, 506, 509, 510, 511, 512, 514, 521, 522, 523, 528, 529, 530, 531, 533, 537, 543, 544, 550, 552, 553, 559, 560, 572, 575, 581, 582, 586, 590, 591, 595, 597, 598, 599, 602, 606, 607, 610, 611, 612, 614, 616, 620, 624, 626, 630, 632, 633, 634, 635, 636, 639, 641, 642, 645, 646, 652, 654, 665, 666, 667, 668, 670, 671, 672, 673, 674, 677, 681, 682, 687, 688, 690, 692, 693, 695, 697, 700, 707, 710, 712, 714, 717, 718, 726, 730, 733, 735, 737, 738, 740, 742, 749, 751, 755, 757, 761, 762, 765, 766, 772, 776, 780, 784, 785, 786, 787, 788, 790, 794, 799, 801, 802, 803, 805, 807, 817, 819, 821, 822, 823, 825, 835, 836, 839, 840, 842, 849, 851, 852, 859, 860, 861, 862, 866, 867, 869, 870, 871, 878, 879, 882, 883, 884, 887, 888, 889, 892, 893, 898, 902, 903, 904, 905, 910, 917, 919, 923, 924, 927, 932, 933, 935, 937, 940, 942, 945, 955, 956, 958, 959, 960, 963, 976, 979, 982, 983, 986, 990, 992, 993, 1000} We remove these balls and are now left with, 628, balls The, 628, balls landed in the following cells [110, 197, 929, 547, 734, 63, 498, 593, 962, 648, 867, 510, 414, 472, 768, 385, 315, 648, 398, 373, 713, 683, 715, 23, 713, 320, 15, 979, 385, 94, 529, 245, 210, 323, 754, 580, 585, 427, 756, 633, 137, 236, 696, 946, 639, 108, 458, 848, 9, 596, 903, 201, 8, 996, 274, 900, 154, 408, 219, 564, 184, 874, 536, 270, 496, 235, 97, 545, 751, 188, 620, 696, 131, 477, 747, 435, 820, 294, 948, 882, 279, 638, 846, 62, 775, 66, 547, 437, 571, 136, 299, 573, 591, 684, 435, 998, 961, 887, 888, 717, 835, 96, 905, 591, 810, 989, 934, 980, 824, 82, 68, 815, 582, 258, 617, 508, 303, 140, 418, 245, 301, 665, 104, 335, 137, 10, 709, 886, 643, 392, 686, 66, 443, 239, 889, 296, 478, 122, 613, 835, 802, 574, 417, 186, 502, 820, 880, 696, 145, 859, 141, 974, 614, 926, 853, 280, 880, 774, 959, 732, 112, 957, 83, 181, 596, 433, 494, 70, 761, 466, 903, 714, 446, 562, 803, 897, 118, 830, 813, 649, 792, 320, 653, 956, 836, 632, 201, 985, 190, 40, 559, 275, 405, 247, 980, 672, 596, 270, 698, 41, 370, 217, 975, 277, 203, 846, 93, 998, 149, 114, 631, 795, 733, 819, 831, 163, 664, 925, 781, 36, 115, 595, 377, 121, 790, 953, 212, 614, 474, 143, 669, 812, 769, 488, 662, 991, 548, 659, 706, 46, 779, 310, 851, 276, 213, 295, 834, 859, 429, 970, 921, 648, 543, 907, 282, 70, 945, 929, 101, 692, 760, 128, 489, 596, 844, 988, 521, 299, 149, 973, 327, 149, 437, 813, 121, 519, 124, 420, 513, 728, 601, 708, 488, 256, 338, 208, 30, 997, 352, 596, 901, 97, 534, 796, 8, 927, 722, 343, 304, 465, 531, 668, 706, 881, 170, 624, 914, 159, 245, 674, 427, 499, 681, 891, 924, 859, 190, 227, 974, 917, 747, 385, 162, 328, 830, 227, 41, 114, 708, 777, 25, 523, 482, 991, 325, 189, 726, 631, 913, 818, 424, 964, 662, 628, 728, 321, 85, 913, 421, 733, 673, 122, 289, 951, 251, 947, 583, 432, 229, 604, 683, 89, 483, 871, 89, 98, 254, 675, 894, 990, 155, 119, 64, 88, 947, 585, 401, 994, 767, 479, 599, 144, 215, 728, 712, 484, 80, 503, 211, 744, 767, 32, 487, 831, 425, 235, 558, 477, 469, 234, 115, 306, 486, 102, 457, 481, 241, 111, 712, 913, 66, 649, 786, 119, 199, 299, 79, 445, 566, 886, 918, 983, 841, 767, 332, 586, 535, 824, 928, 261, 750, 78, 308, 661, 881, 237, 360, 459, 83, 54, 653, 924, 528, 231, 221, 899, 632, 588, 906, 586, 642, 793, 967, 594, 100, 154, 188, 497, 584, 686, 731, 172, 859, 661, 855, 493, 418, 861, 833, 851, 982, 177, 564, 711, 994, 51, 967, 551, 167, 567, 549, 151, 81, 598, 317, 510, 648, 174, 409, 753, 1, 456, 900, 371, 80, 523, 964, 490, 830, 235, 985, 693, 384, 353, 292, 688, 526, 902, 478, 87, 466, 575, 475, 747, 201, 830, 14, 105, 99, 686, 570, 621, 411, 983, 907, 58, 4, 244, 85, 673, 286, 575, 605, 875, 136, 896, 867, 531, 527, 224, 19, 114, 935, 399, 97, 313, 645, 728, 880, 384, 734, 93, 410, 638, 435, 666, 563, 982, 660, 726, 521, 778, 434, 381, 358, 948, 597, 158, 306, 225, 301, 514, 9, 537, 488, 955, 13, 835, 529, 117, 176, 359, 647, 782, 499, 51, 38, 817, 30, 708, 325, 500, 580, 40, 862, 632, 506, 333, 485, 600, 509, 182, 578, 123, 454, 349, 655, 870, 941, 466, 267, 867, 780, 25, 280, 454, 694, 915, 87, 105, 719, 377, 523, 663, 875, 538, 629, 591] The set of cells that are occupied is {1, 4, 8, 9, 10, 13, 14, 15, 19, 23, 25, 30, 32, 36, 38, 40, 41, 46, 51, 54, 58, 62, 63, 64, 66, 68, 70, 78, 79, 80, 81, 82, 83, 85, 87, 88, 89, 93, 94, 96, 97, 98, 99, 100, 101, 102, 104, 105, 108, 110, 111, 112, 114, 115, 117, 118, 119, 121, 122, 123, 124, 128, 131, 136, 137, 140, 141, 143, 144, 145, 149, 151, 154, 155, 158, 159, 162, 163, 167, 170, 172, 174, 176, 177, 181, 182, 184, 186, 188, 189, 190, 197, 199, 201, 203, 208, 210, 211, 212, 213, 215, 217, 219, 221, 224, 225, 227, 229, 231, 234, 235, 236, 237, 239, 241, 244, 245, 247, 251, 254, 256, 258, 261, 267, 270, 274, 275, 276, 277, 279, 280, 282, 286, 289, 292, 294, 295, 296, 299, 301, 303, 304, 306, 308, 310, 313, 315, 317, 320, 321, 323, 325, 327, 328, 332, 333, 335, 338, 343, 349, 352, 353, 358, 359, 360, 370, 371, 373, 377, 381, 384, 385, 392, 398, 399, 401, 405, 408, 409, 410, 411, 414, 417, 418, 420, 421, 424, 425, 427, 429, 432, 433, 434, 435, 437, 443, 445, 446, 454, 456, 457, 458, 459, 465, 466, 469, 472, 474, 475, 477, 478, 479, 481, 482, 483, 484, 485, 486, 487, 488, 489, 490, 493, 494, 496, 497, 498, 499, 500, 502, 503, 506, 508, 509, 510, 513, 514, 519, 521, 523, 526, 527, 528, 529, 531, 534, 535, 536, 537, 538, 543, 545, 547, 548, 549, 551, 558, 559, 562, 563, 564, 566, 567, 570, 571, 573, 574, 575, 578, 580, 582, 583, 584, 585, 586, 588, 591, 593, 594, 595, 596, 597, 598, 599, 600, 601, 604, 605, 613, 614, 617, 620, 621, 624, 628, 629, 631, 632, 633, 638, 639, 642, 643, 645, 647, 648, 649, 653, 655, 659, 660, 661, 662, 663, 664, 665, 666, 668, 669, 672, 673, 674, 675, 681, 683, 684, 686, 688, 692, 693, 694, 696, 698, 706, 708, 709, 711, 712, 713, 714, 715, 717, 719, 722, 726, 728, 731, 732, 733, 734, 744, 747, 750, 751, 753, 754, 756, 760, 761, 767, 768, 769, 774, 775, 777, 778, 779, 780, 781, 782, 786, 790, 792, 793, 795, 796, 802, 803, 810, 812, 813, 815, 817, 818, 819, 820, 824, 830, 831, 833, 834, 835, 836, 841, 844, 846, 848, 851, 853, 855, 859, 861, 862, 867, 870, 871, 874, 875, 880, 881, 882, 886, 887, 888, 889, 891, 894, 896, 897, 899, 900, 901, 902, 903, 905, 906, 907, 913, 914, 915, 917, 918, 921, 924, 925, 926, 927, 928, 929, 934, 935, 941, 945, 946, 947, 948, 951, 953, 955, 956, 957, 959, 961, 962, 964, 967, 970, 973, 974, 975, 979, 980, 982, 983, 985, 988, 989, 990, 991, 994, 996, 997, 998} The set of cells that have exactly one ball in them is {1, 4, 10, 13, 14, 15, 19, 23, 32, 36, 38, 46, 54, 58, 62, 63, 64, 68, 78, 79, 81, 82, 88, 94, 96, 98, 99, 100, 101, 102, 104, 108, 110, 111, 112, 117, 118, 123, 124, 128, 131, 140, 141, 143, 144, 145, 151, 155, 158, 159, 162, 163, 167, 170, 172, 174, 176, 177, 181, 182, 184, 186, 189, 197, 199, 203, 208, 210, 211, 212, 213, 215, 217, 219, 221, 224, 225, 229, 231, 234, 236, 237, 239, 241, 244, 247, 251, 254, 256, 258, 261, 267, 274, 275, 276, 277, 279, 282, 286, 289, 292, 294, 295, 296, 303, 304, 308, 310, 313, 315, 317, 321, 323, 327, 328, 332, 333, 335, 338, 343, 349, 352, 353, 358, 359, 360, 370, 371, 373, 381, 392, 398, 399, 401, 405, 408, 409, 410, 411, 414, 417, 420, 421, 424, 425, 429, 432, 433, 434, 443, 445, 446, 456, 457, 458, 459, 465, 469, 472, 474, 475, 479, 481, 482, 483, 484, 485, 486, 487, 489, 490, 493, 494, 496, 497, 498, 500, 502, 503, 506, 508, 509, 513, 514, 519, 526, 527, 528, 534, 535, 536, 537, 538, 543, 545, 548, 549, 551, 558, 559, 562, 563, 566, 567, 570, 571, 573, 574, 578, 582, 583, 584, 588, 593, 594, 595, 597, 598, 599, 600, 601, 604, 605, 613, 617, 620, 621, 624, 628, 629, 633, 639, 642, 643, 645, 647, 655, 659, 660, 663, 664, 665, 666, 668, 669, 672, 674, 675, 681, 684, 688, 692, 693, 694, 698, 709, 711, 714, 715, 717, 719, 722, 731, 732, 744, 750, 751, 753, 754, 756, 760, 761, 768, 769, 774, 775, 777, 778, 779, 780, 781, 782, 786, 790, 792, 793, 795, 796, 802, 803, 810, 812, 815, 817, 818, 819, 833, 834, 836, 841, 844, 848, 853, 855, 861, 862, 870, 871, 874, 882, 887, 888, 889, 891, 894, 896, 897, 899, 901, 902, 905, 906, 914, 915, 917, 918, 921, 925, 926, 927, 928, 934, 935, 941, 945, 946, 951, 953, 955, 956, 957, 959, 961, 962, 970, 973, 975, 979, 988, 989, 990, 996, 997} We remove these balls and are now left with, 275, balls The, 275, balls landed in the following cells [617, 185, 829, 301, 898, 437, 472, 973, 630, 73, 844, 728, 752, 94, 410, 637, 10, 445, 858, 210, 782, 837, 160, 900, 15, 77, 629, 188, 203, 640, 634, 574, 795, 618, 270, 216, 793, 99, 69, 727, 378, 388, 695, 256, 449, 852, 270, 372, 440, 610, 885, 959, 245, 816, 976, 914, 538, 906, 555, 957, 609, 305, 660, 41, 669, 446, 535, 588, 546, 581, 503, 387, 987, 435, 81, 246, 880, 776, 839, 972, 598, 180, 564, 465, 986, 64, 417, 858, 347, 170, 518, 901, 981, 966, 169, 458, 137, 634, 797, 477, 979, 495, 960, 485, 650, 774, 732, 904, 878, 95, 750, 124, 952, 447, 819, 228, 435, 831, 55, 668, 134, 46, 167, 196, 229, 285, 392, 55, 835, 52, 668, 336, 835, 398, 568, 297, 352, 760, 104, 745, 598, 272, 202, 273, 741, 364, 342, 464, 474, 429, 691, 864, 329, 66, 970, 185, 156, 312, 432, 184, 262, 117, 964, 552, 441, 913, 5, 920, 290, 42, 828, 262, 671, 139, 759, 590, 495, 469, 891, 554, 923, 875, 479, 516, 675, 719, 455, 292, 6, 517, 856, 453, 891, 589, 262, 39, 731, 582, 81, 655, 285, 390, 463, 161, 401, 400, 696, 813, 841, 338, 473, 898, 632, 122, 642, 425, 61, 903, 366, 839, 141, 355, 473, 346, 158, 375, 793, 39, 652, 511, 530, 556, 591, 645, 171, 572, 948, 388, 29, 478, 484, 866, 621, 821, 211, 336, 58, 163, 702, 648, 107, 189, 36, 158, 213, 254, 545, 695, 52, 613, 211, 581, 126, 675, 291, 795, 377, 910, 266, 716, 134, 425, 636, 65, 591] The set of cells that are occupied is {5, 6, 10, 15, 29, 36, 39, 41, 42, 46, 52, 55, 58, 61, 64, 65, 66, 69, 73, 77, 81, 94, 95, 99, 104, 107, 117, 122, 124, 126, 134, 137, 139, 141, 156, 158, 160, 161, 163, 167, 169, 170, 171, 180, 184, 185, 188, 189, 196, 202, 203, 210, 211, 213, 216, 228, 229, 245, 246, 254, 256, 262, 266, 270, 272, 273, 285, 290, 291, 292, 297, 301, 305, 312, 329, 336, 338, 342, 346, 347, 352, 355, 364, 366, 372, 375, 377, 378, 387, 388, 390, 392, 398, 400, 401, 410, 417, 425, 429, 432, 435, 437, 440, 441, 445, 446, 447, 449, 453, 455, 458, 463, 464, 465, 469, 472, 473, 474, 477, 478, 479, 484, 485, 495, 503, 511, 516, 517, 518, 530, 535, 538, 545, 546, 552, 554, 555, 556, 564, 568, 572, 574, 581, 582, 588, 589, 590, 591, 598, 609, 610, 613, 617, 618, 621, 629, 630, 632, 634, 636, 637, 640, 642, 645, 648, 650, 652, 655, 660, 668, 669, 671, 675, 691, 695, 696, 702, 716, 719, 727, 728, 731, 732, 741, 745, 750, 752, 759, 760, 774, 776, 782, 793, 795, 797, 813, 816, 819, 821, 828, 829, 831, 835, 837, 839, 841, 844, 852, 856, 858, 864, 866, 875, 878, 880, 885, 891, 898, 900, 901, 903, 904, 906, 910, 913, 914, 920, 923, 948, 952, 957, 959, 960, 964, 966, 970, 972, 973, 976, 979, 981, 986, 987} The set of cells that have exactly one ball in them is {5, 6, 10, 15, 29, 36, 41, 42, 46, 58, 61, 64, 65, 66, 69, 73, 77, 94, 95, 99, 104, 107, 117, 122, 124, 126, 137, 139, 141, 156, 160, 161, 163, 167, 169, 170, 171, 180, 184, 188, 189, 196, 202, 203, 210, 213, 216, 228, 229, 245, 246, 254, 256, 266, 272, 273, 290, 291, 292, 297, 301, 305, 312, 329, 338, 342, 346, 347, 352, 355, 364, 366, 372, 375, 377, 378, 387, 390, 392, 398, 400, 401, 410, 417, 429, 432, 437, 440, 441, 445, 446, 447, 449, 453, 455, 458, 463, 464, 465, 469, 472, 474, 477, 478, 479, 484, 485, 503, 511, 516, 517, 518, 530, 535, 538, 545, 546, 552, 554, 555, 556, 564, 568, 572, 574, 582, 588, 589, 590, 609, 610, 613, 617, 618, 621, 629, 630, 632, 636, 637, 640, 642, 645, 648, 650, 652, 655, 660, 669, 671, 691, 696, 702, 716, 719, 727, 728, 731, 732, 741, 745, 750, 752, 759, 760, 774, 776, 782, 797, 813, 816, 819, 821, 828, 829, 831, 837, 841, 844, 852, 856, 864, 866, 875, 878, 880, 885, 900, 901, 903, 904, 906, 910, 913, 914, 920, 923, 948, 952, 957, 959, 960, 964, 966, 970, 972, 973, 976, 979, 981, 986, 987} We remove these balls and are now left with, 63, balls The, 63, balls landed in the following cells [215, 126, 496, 547, 145, 614, 376, 461, 738, 543, 587, 389, 104, 872, 458, 206, 816, 174, 552, 906, 794, 804, 578, 318, 790, 950, 517, 445, 527, 767, 155, 504, 857, 579, 564, 383, 580, 981, 930, 869, 977, 865, 430, 65, 758, 899, 52, 458, 695, 892, 456, 798, 957, 661, 655, 789, 483, 283, 797, 11, 54, 96, 440] The set of cells that are occupied is {11, 52, 54, 65, 96, 104, 126, 145, 155, 174, 206, 215, 283, 318, 376, 383, 389, 430, 440, 445, 456, 458, 461, 483, 496, 504, 517, 527, 543, 547, 552, 564, 578, 579, 580, 587, 614, 655, 661, 695, 738, 758, 767, 789, 790, 794, 797, 798, 804, 816, 857, 865, 869, 872, 892, 899, 906, 930, 950, 957, 977, 981} The set of cells that have exactly one ball in them is {11, 52, 54, 65, 96, 104, 126, 145, 155, 174, 206, 215, 283, 318, 376, 383, 389, 430, 440, 445, 456, 461, 483, 496, 504, 517, 527, 543, 547, 552, 564, 578, 579, 580, 587, 614, 655, 661, 695, 738, 758, 767, 789, 790, 794, 797, 798, 804, 816, 857, 865, 869, 872, 892, 899, 906, 930, 950, 957, 977, 981} We remove these balls and are now left with, 2, balls The, 2, balls landed in the following cells [719, 927] The set of cells that are occupied is {719, 927} The set of cells that have exactly one ball in them is {719, 927} We remove these balls and are now left with, 0, balls This took, 5, rounds The, 1000, balls landed in the following cells [951, 707, 267, 231, 108, 20, 696, 51, 400, 737, 768, 308, 445, 889, 232, 983, 420, 587, 607, 233, 814, 905, 856, 228, 179, 812, 686, 648, 583, 461, 134, 268, 238, 502, 186, 902, 558, 979, 637, 855, 437, 888, 191, 341, 210, 167, 147, 818, 998, 913, 839, 999, 839, 240, 253, 336, 555, 110, 706, 23, 183, 76, 1000, 460, 653, 583, 788, 469, 160, 872, 214, 156, 547, 718, 574, 586, 13, 919, 661, 637, 392, 242, 923, 863, 132, 444, 614, 866, 124, 204, 721, 378, 997, 555, 594, 768, 788, 899, 931, 117, 633, 548, 716, 171, 385, 748, 337, 321, 651, 710, 22, 959, 937, 362, 224, 390, 203, 263, 954, 560, 199, 312, 152, 545, 903, 919, 756, 817, 638, 954, 901, 179, 325, 665, 668, 177, 312, 603, 459, 254, 549, 832, 757, 571, 339, 720, 629, 239, 388, 270, 715, 122, 788, 951, 566, 109, 884, 955, 425, 92, 593, 495, 919, 284, 901, 173, 939, 86, 43, 321, 433, 491, 126, 244, 950, 784, 275, 628, 330, 392, 43, 991, 407, 475, 861, 309, 514, 783, 996, 600, 410, 497, 454, 211, 652, 564, 470, 167, 96, 629, 465, 620, 736, 514, 688, 72, 691, 7, 832, 682, 391, 301, 614, 172, 573, 918, 498, 434, 842, 567, 545, 84, 766, 347, 115, 186, 60, 89, 572, 295, 425, 37, 304, 16, 185, 14, 155, 581, 656, 134, 854, 723, 720, 64, 283, 196, 87, 965, 259, 934, 425, 260, 388, 23, 249, 849, 405, 478, 910, 536, 280, 980, 929, 108, 312, 307, 405, 377, 900, 570, 893, 533, 643, 902, 179, 78, 622, 877, 536, 746, 583, 173, 56, 310, 206, 607, 65, 677, 806, 583, 799, 924, 105, 93, 995, 603, 419, 716, 397, 374, 76, 961, 328, 342, 390, 696, 772, 534, 784, 485, 85, 781, 593, 234, 525, 244, 551, 854, 424, 872, 76, 495, 680, 316, 68, 574, 908, 471, 958, 635, 455, 811, 771, 374, 107, 101, 29, 182, 678, 315, 757, 174, 178, 163, 917, 447, 133, 903, 380, 222, 365, 762, 237, 135, 931, 514, 264, 713, 112, 937, 573, 867, 239, 804, 669, 366, 311, 922, 920, 36, 457, 378, 996, 576, 344, 625, 241, 774, 5, 358, 848, 990, 992, 584, 788, 640, 416, 519, 438, 228, 565, 134, 604, 995, 980, 423, 882, 22, 87, 63, 963, 968, 140, 510, 29, 625, 905, 24, 304, 21, 52, 62, 133, 322, 412, 492, 989, 127, 951, 195, 981, 725, 887, 44, 744, 531, 805, 585, 507, 266, 419, 123, 831, 47, 284, 360, 357, 973, 202, 505, 44, 1000, 849, 718, 997, 13, 474, 894, 883, 452, 982, 734, 12, 42, 555, 884, 39, 445, 125, 725, 654, 530, 683, 488, 267, 737, 952, 261, 494, 71, 323, 648, 807, 540, 919, 608, 965, 310, 900, 261, 784, 416, 776, 702, 923, 862, 423, 785, 843, 250, 811, 529, 789, 26, 537, 725, 749, 274, 308, 553, 931, 47, 336, 596, 995, 594, 199, 55, 368, 552, 442, 845, 839, 736, 144, 657, 167, 352, 521, 892, 959, 199, 411, 366, 364, 40, 733, 428, 282, 321, 316, 106, 855, 580, 34, 22, 807, 295, 357, 900, 912, 61, 415, 808, 370, 393, 767, 380, 795, 994, 617, 384, 915, 252, 623, 231, 858, 425, 476, 306, 268, 713, 400, 851, 832, 58, 938, 197, 943, 743, 718, 448, 19, 44, 575, 379, 315, 320, 837, 52, 636, 973, 380, 68, 962, 852, 271, 498, 998, 737, 151, 742, 153, 442, 227, 218, 436, 793, 116, 713, 336, 200, 591, 327, 317, 150, 422, 180, 555, 78, 646, 279, 92, 98, 271, 490, 676, 181, 931, 110, 312, 751, 624, 56, 824, 427, 395, 702, 924, 807, 935, 83, 79, 57, 706, 994, 884, 668, 895, 708, 416, 291, 713, 54, 519, 316, 942, 183, 488, 814, 478, 623, 672, 506, 36, 278, 630, 790, 201, 175, 583, 349, 369, 583, 893, 244, 719, 686, 81, 715, 763, 702, 271, 546, 92, 886, 571, 316, 424, 909, 920, 201, 178, 840, 799, 480, 969, 602, 808, 673, 848, 136, 321, 167, 36, 912, 447, 464, 750, 618, 470, 375, 273, 716, 760, 652, 44, 378, 657, 618, 444, 978, 218, 596, 941, 147, 84, 496, 556, 81, 204, 405, 180, 719, 521, 523, 310, 859, 153, 584, 627, 750, 153, 86, 154, 349, 561, 246, 239, 78, 645, 320, 113, 629, 884, 241, 582, 38, 106, 677, 422, 624, 939, 707, 174, 323, 498, 391, 456, 996, 143, 203, 785, 205, 936, 860, 226, 770, 985, 612, 993, 147, 901, 784, 102, 241, 709, 725, 394, 5, 337, 4, 661, 409, 723, 329, 671, 298, 911, 781, 966, 621, 993, 301, 156, 223, 65, 205, 79, 277, 682, 466, 755, 92, 443, 216, 572, 320, 86, 929, 899, 521, 367, 2, 364, 306, 959, 56, 460, 88, 649, 160, 1, 989, 706, 106, 880, 15, 810, 234, 711, 970, 655, 584, 737, 73, 139, 312, 444, 699, 116, 745, 241, 559, 889, 167, 271, 426, 379, 521, 438, 84, 435, 371, 313, 435, 154, 495, 401, 499, 606, 162, 821, 134, 431, 68, 361, 63, 558, 654, 785, 640, 656, 738, 627, 164, 830, 691, 69, 573, 708, 823, 667, 188, 773, 74, 592, 410, 493, 894, 338, 737, 688, 436, 281, 731, 324, 98, 825, 237, 352, 603, 126, 366, 649, 661, 846, 853, 699, 736, 54, 238, 301, 450, 732, 400, 327, 535, 607, 221, 66, 574, 318, 458, 413, 801, 358, 174, 388, 463, 651, 393, 810, 440, 710, 80, 379, 985, 771, 111, 595, 196, 137, 612, 227, 461, 208, 244, 554, 846, 234, 207, 831, 565, 117, 4, 174, 40, 875, 778, 533, 898, 451, 676, 194, 339, 669, 943, 592, 881, 775, 874, 125, 162, 645, 297, 805, 211, 608, 806, 740, 49, 20, 308, 349, 954, 46, 47, 337, 591, 937, 492, 350, 770, 325, 597, 94, 839, 504, 911] The set of cells that are occupied is {1, 2, 4, 5, 7, 12, 13, 14, 15, 16, 19, 20, 21, 22, 23, 24, 26, 29, 34, 36, 37, 38, 39, 40, 42, 43, 44, 46, 47, 49, 51, 52, 54, 55, 56, 57, 58, 60, 61, 62, 63, 64, 65, 66, 68, 69, 71, 72, 73, 74, 76, 78, 79, 80, 81, 83, 84, 85, 86, 87, 88, 89, 92, 93, 94, 96, 98, 101, 102, 105, 106, 107, 108, 109, 110, 111, 112, 113, 115, 116, 117, 122, 123, 124, 125, 126, 127, 132, 133, 134, 135, 136, 137, 139, 140, 143, 144, 147, 150, 151, 152, 153, 154, 155, 156, 160, 162, 163, 164, 167, 171, 172, 173, 174, 175, 177, 178, 179, 180, 181, 182, 183, 185, 186, 188, 191, 194, 195, 196, 197, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 210, 211, 214, 216, 218, 221, 222, 223, 224, 226, 227, 228, 231, 232, 233, 234, 237, 238, 239, 240, 241, 242, 244, 246, 249, 250, 252, 253, 254, 259, 260, 261, 263, 264, 266, 267, 268, 270, 271, 273, 274, 275, 277, 278, 279, 280, 281, 282, 283, 284, 291, 295, 297, 298, 301, 304, 306, 307, 308, 309, 310, 311, 312, 313, 315, 316, 317, 318, 320, 321, 322, 323, 324, 325, 327, 328, 329, 330, 336, 337, 338, 339, 341, 342, 344, 347, 349, 350, 352, 357, 358, 360, 361, 362, 364, 365, 366, 367, 368, 369, 370, 371, 374, 375, 377, 378, 379, 380, 384, 385, 388, 390, 391, 392, 393, 394, 395, 397, 400, 401, 405, 407, 409, 410, 411, 412, 413, 415, 416, 419, 420, 422, 423, 424, 425, 426, 427, 428, 431, 433, 434, 435, 436, 437, 438, 440, 442, 443, 444, 445, 447, 448, 450, 451, 452, 454, 455, 456, 457, 458, 459, 460, 461, 463, 464, 465, 466, 469, 470, 471, 474, 475, 476, 478, 480, 485, 488, 490, 491, 492, 493, 494, 495, 496, 497, 498, 499, 502, 504, 505, 506, 507, 510, 514, 519, 521, 523, 525, 529, 530, 531, 533, 534, 535, 536, 537, 540, 545, 546, 547, 548, 549, 551, 552, 553, 554, 555, 556, 558, 559, 560, 561, 564, 565, 566, 567, 570, 571, 572, 573, 574, 575, 576, 580, 581, 582, 583, 584, 585, 586, 587, 591, 592, 593, 594, 595, 596, 597, 600, 602, 603, 604, 606, 607, 608, 612, 614, 617, 618, 620, 621, 622, 623, 624, 625, 627, 628, 629, 630, 633, 635, 636, 637, 638, 640, 643, 645, 646, 648, 649, 651, 652, 653, 654, 655, 656, 657, 661, 665, 667, 668, 669, 671, 672, 673, 676, 677, 678, 680, 682, 683, 686, 688, 691, 696, 699, 702, 706, 707, 708, 709, 710, 711, 713, 715, 716, 718, 719, 720, 721, 723, 725, 731, 732, 733, 734, 736, 737, 738, 740, 742, 743, 744, 745, 746, 748, 749, 750, 751, 755, 756, 757, 760, 762, 763, 766, 767, 768, 770, 771, 772, 773, 774, 775, 776, 778, 781, 783, 784, 785, 788, 789, 790, 793, 795, 799, 801, 804, 805, 806, 807, 808, 810, 811, 812, 814, 817, 818, 821, 823, 824, 825, 830, 831, 832, 837, 839, 840, 842, 843, 845, 846, 848, 849, 851, 852, 853, 854, 855, 856, 858, 859, 860, 861, 862, 863, 866, 867, 872, 874, 875, 877, 880, 881, 882, 883, 884, 886, 887, 888, 889, 892, 893, 894, 895, 898, 899, 900, 901, 902, 903, 905, 908, 909, 910, 911, 912, 913, 915, 917, 918, 919, 920, 922, 923, 924, 929, 931, 934, 935, 936, 937, 938, 939, 941, 942, 943, 950, 951, 952, 954, 955, 958, 959, 961, 962, 963, 965, 966, 968, 969, 970, 973, 978, 979, 980, 981, 982, 983, 985, 989, 990, 991, 992, 993, 994, 995, 996, 997, 998, 999, 1000} The set of cells that have exactly one ball in them is {1, 2, 7, 12, 14, 15, 16, 19, 21, 24, 26, 34, 37, 38, 39, 42, 46, 49, 51, 55, 57, 58, 60, 61, 62, 64, 66, 69, 71, 72, 73, 74, 80, 83, 85, 88, 89, 93, 94, 96, 101, 102, 105, 107, 109, 111, 112, 113, 115, 122, 123, 124, 127, 132, 135, 136, 137, 139, 140, 143, 144, 150, 151, 152, 155, 163, 164, 171, 172, 175, 177, 181, 182, 185, 188, 191, 194, 195, 197, 200, 202, 206, 207, 208, 210, 214, 216, 221, 222, 223, 224, 226, 232, 233, 240, 242, 246, 249, 250, 252, 253, 254, 259, 260, 263, 264, 266, 270, 273, 274, 275, 277, 278, 279, 280, 281, 282, 283, 291, 297, 298, 307, 309, 311, 313, 317, 318, 322, 324, 328, 329, 330, 338, 341, 342, 344, 347, 350, 360, 361, 362, 365, 367, 368, 369, 370, 371, 375, 377, 384, 385, 394, 395, 397, 401, 407, 409, 411, 412, 413, 415, 420, 426, 427, 428, 431, 433, 434, 437, 440, 443, 448, 450, 451, 452, 454, 455, 456, 457, 458, 459, 463, 464, 465, 466, 469, 471, 474, 475, 476, 480, 485, 490, 491, 493, 494, 496, 497, 499, 502, 504, 505, 506, 507, 510, 523, 525, 529, 530, 531, 534, 535, 537, 540, 546, 547, 548, 549, 551, 552, 553, 554, 556, 559, 560, 561, 564, 566, 567, 570, 575, 576, 580, 581, 582, 585, 586, 587, 595, 597, 600, 602, 604, 606, 617, 620, 621, 622, 628, 630, 633, 635, 636, 638, 643, 646, 653, 655, 665, 667, 671, 672, 673, 678, 680, 683, 709, 711, 721, 731, 732, 733, 734, 738, 740, 742, 743, 744, 745, 746, 748, 749, 751, 755, 756, 760, 762, 763, 766, 767, 772, 773, 774, 775, 776, 778, 783, 789, 790, 793, 795, 801, 804, 812, 817, 818, 821, 823, 824, 825, 830, 837, 840, 842, 843, 845, 851, 852, 853, 856, 858, 859, 860, 861, 862, 863, 866, 867, 874, 875, 877, 880, 881, 882, 883, 886, 887, 888, 892, 895, 898, 908, 909, 910, 913, 915, 917, 918, 922, 934, 935, 936, 938, 941, 942, 950, 952, 955, 958, 961, 962, 963, 966, 968, 969, 970, 978, 979, 981, 982, 983, 990, 991, 992, 999} We remove these balls and are now left with, 625, balls The, 625, balls landed in the following cells [840, 622, 606, 792, 189, 72, 233, 839, 522, 891, 691, 700, 477, 32, 177, 394, 360, 923, 450, 811, 81, 39, 359, 984, 325, 111, 84, 128, 427, 375, 180, 266, 536, 102, 462, 244, 114, 651, 86, 285, 432, 30, 9, 453, 195, 668, 925, 898, 785, 727, 575, 999, 182, 971, 6, 335, 728, 465, 451, 705, 625, 507, 468, 1, 267, 82, 680, 102, 161, 373, 645, 295, 961, 256, 531, 460, 505, 903, 413, 822, 855, 177, 317, 330, 772, 803, 470, 44, 41, 929, 178, 607, 928, 969, 132, 179, 114, 374, 865, 786, 431, 768, 506, 969, 899, 632, 556, 396, 974, 943, 7, 54, 51, 820, 439, 405, 673, 960, 191, 449, 301, 647, 184, 426, 254, 327, 595, 468, 76, 951, 827, 475, 541, 547, 719, 564, 229, 401, 977, 790, 200, 281, 715, 663, 218, 428, 175, 372, 411, 814, 391, 938, 462, 331, 690, 868, 569, 957, 434, 960, 588, 903, 186, 416, 773, 315, 471, 949, 374, 26, 376, 354, 975, 899, 801, 695, 71, 157, 865, 538, 142, 173, 349, 498, 844, 456, 404, 846, 82, 710, 778, 99, 714, 105, 84, 588, 415, 533, 845, 37, 655, 153, 31, 468, 761, 653, 740, 715, 423, 69, 60, 5, 834, 706, 222, 329, 791, 817, 923, 747, 790, 632, 842, 917, 829, 40, 209, 995, 926, 941, 170, 718, 862, 95, 676, 797, 288, 474, 749, 430, 832, 151, 78, 334, 345, 499, 526, 374, 772, 716, 372, 263, 208, 915, 230, 909, 373, 384, 355, 131, 569, 465, 267, 436, 248, 820, 888, 295, 834, 733, 749, 882, 949, 951, 9, 974, 426, 905, 916, 41, 723, 455, 489, 323, 134, 921, 542, 354, 48, 550, 418, 818, 460, 573, 542, 932, 724, 59, 32, 71, 537, 452, 202, 864, 291, 622, 502, 492, 619, 95, 385, 666, 962, 245, 82, 721, 355, 193, 766, 945, 982, 2, 208, 725, 19, 385, 448, 288, 746, 615, 729, 892, 571, 391, 677, 440, 716, 883, 988, 532, 251, 213, 117, 578, 485, 904, 481, 756, 358, 580, 566, 562, 981, 34, 286, 341, 840, 420, 917, 577, 168, 168, 214, 817, 809, 566, 983, 469, 9, 96, 498, 845, 106, 892, 639, 387, 508, 915, 66, 547, 297, 722, 581, 981, 266, 213, 949, 674, 304, 561, 330, 704, 197, 9, 218, 492, 202, 759, 540, 246, 305, 116, 452, 484, 457, 557, 462, 482, 65, 709, 537, 469, 713, 830, 388, 993, 966, 976, 519, 833, 793, 202, 279, 479, 908, 362, 906, 993, 347, 107, 303, 997, 352, 464, 624, 161, 127, 421, 850, 146, 377, 254, 750, 292, 994, 429, 378, 993, 856, 138, 356, 272, 319, 232, 560, 930, 670, 705, 915, 124, 577, 347, 119, 579, 466, 650, 683, 598, 26, 556, 962, 502, 741, 556, 746, 62, 585, 412, 247, 545, 129, 873, 536, 155, 962, 527, 681, 205, 805, 788, 924, 743, 791, 539, 766, 349, 796, 780, 349, 945, 641, 815, 377, 827, 20, 627, 433, 346, 17, 47, 230, 572, 869, 491, 66, 245, 672, 66, 361, 380, 34, 659, 748, 734, 565, 906, 594, 892, 940, 256, 384, 310, 987, 257, 326, 986, 472, 969, 18, 924, 557, 304, 174, 484, 55, 862, 830, 990, 581, 256, 586, 965, 298, 478, 703, 554, 317, 540, 833, 204, 486, 296, 110, 772, 308, 190, 121, 226, 664, 729, 525, 81, 397, 735, 576, 673, 490, 496, 54, 60, 559, 752, 177, 138, 442, 377, 305, 234, 854, 9, 256, 988, 378, 643, 38, 919, 115, 394, 231, 715, 736, 208, 206, 560, 59, 465, 493, 986, 547, 474, 194, 256, 570, 869, 947, 394, 181, 144, 892, 488, 307, 626, 365, 576, 236] The set of cells that are occupied is {1, 2, 5, 6, 7, 9, 17, 18, 19, 20, 26, 30, 31, 32, 34, 37, 38, 39, 40, 41, 44, 47, 48, 51, 54, 55, 59, 60, 62, 65, 66, 69, 71, 72, 76, 78, 81, 82, 84, 86, 95, 96, 99, 102, 105, 106, 107, 110, 111, 114, 115, 116, 117, 119, 121, 124, 127, 128, 129, 131, 132, 134, 138, 142, 144, 146, 151, 153, 155, 157, 161, 168, 170, 173, 174, 175, 177, 178, 179, 180, 181, 182, 184, 186, 189, 190, 191, 193, 194, 195, 197, 200, 202, 204, 205, 206, 208, 209, 213, 214, 218, 222, 226, 229, 230, 231, 232, 233, 234, 236, 244, 245, 246, 247, 248, 251, 254, 256, 257, 263, 266, 267, 272, 279, 281, 285, 286, 288, 291, 292, 295, 296, 297, 298, 301, 303, 304, 305, 307, 308, 310, 315, 317, 319, 323, 325, 326, 327, 329, 330, 331, 334, 335, 341, 345, 346, 347, 349, 352, 354, 355, 356, 358, 359, 360, 361, 362, 365, 372, 373, 374, 375, 376, 377, 378, 380, 384, 385, 387, 388, 391, 394, 396, 397, 401, 404, 405, 411, 412, 413, 415, 416, 418, 420, 421, 423, 426, 427, 428, 429, 430, 431, 432, 433, 434, 436, 439, 440, 442, 448, 449, 450, 451, 452, 453, 455, 456, 457, 460, 462, 464, 465, 466, 468, 469, 470, 471, 472, 474, 475, 477, 478, 479, 481, 482, 484, 485, 486, 488, 489, 490, 491, 492, 493, 496, 498, 499, 502, 505, 506, 507, 508, 519, 522, 525, 526, 527, 531, 532, 533, 536, 537, 538, 539, 540, 541, 542, 545, 547, 550, 554, 556, 557, 559, 560, 561, 562, 564, 565, 566, 569, 570, 571, 572, 573, 575, 576, 577, 578, 579, 580, 581, 585, 586, 588, 594, 595, 598, 606, 607, 615, 619, 622, 624, 625, 626, 627, 632, 639, 641, 643, 645, 647, 650, 651, 653, 655, 659, 663, 664, 666, 668, 670, 672, 673, 674, 676, 677, 680, 681, 683, 690, 691, 695, 700, 703, 704, 705, 706, 709, 710, 713, 714, 715, 716, 718, 719, 721, 722, 723, 724, 725, 727, 728, 729, 733, 734, 735, 736, 740, 741, 743, 746, 747, 748, 749, 750, 752, 756, 759, 761, 766, 768, 772, 773, 778, 780, 785, 786, 788, 790, 791, 792, 793, 796, 797, 801, 803, 805, 809, 811, 814, 815, 817, 818, 820, 822, 827, 829, 830, 832, 833, 834, 839, 840, 842, 844, 845, 846, 850, 854, 855, 856, 862, 864, 865, 868, 869, 873, 882, 883, 888, 891, 892, 898, 899, 903, 904, 905, 906, 908, 909, 915, 916, 917, 919, 921, 923, 924, 925, 926, 928, 929, 930, 932, 938, 940, 941, 943, 945, 947, 949, 951, 957, 960, 961, 962, 965, 966, 969, 971, 974, 975, 976, 977, 981, 982, 983, 984, 986, 987, 988, 990, 993, 994, 995, 997, 999} The set of cells that have exactly one ball in them is {1, 2, 5, 6, 7, 17, 18, 19, 20, 30, 31, 37, 38, 39, 40, 44, 47, 48, 51, 55, 62, 65, 69, 72, 76, 78, 86, 96, 99, 105, 106, 107, 110, 111, 115, 116, 117, 119, 121, 124, 127, 128, 129, 131, 132, 134, 142, 144, 146, 151, 153, 155, 157, 170, 173, 174, 175, 178, 179, 180, 181, 182, 184, 186, 189, 190, 191, 193, 194, 195, 197, 200, 204, 205, 206, 209, 214, 222, 226, 229, 231, 232, 233, 234, 236, 244, 246, 247, 248, 251, 257, 263, 272, 279, 281, 285, 286, 291, 292, 296, 297, 298, 301, 303, 307, 308, 310, 315, 319, 323, 325, 326, 327, 329, 331, 334, 335, 341, 345, 346, 352, 356, 358, 359, 360, 361, 362, 365, 375, 376, 380, 387, 388, 396, 397, 401, 404, 405, 411, 412, 413, 415, 416, 418, 420, 421, 423, 427, 428, 429, 430, 431, 432, 433, 434, 436, 439, 440, 442, 448, 449, 450, 451, 453, 455, 456, 457, 464, 466, 470, 471, 472, 475, 477, 478, 479, 481, 482, 485, 486, 488, 489, 490, 491, 493, 496, 499, 505, 506, 507, 508, 519, 522, 525, 526, 527, 531, 532, 533, 538, 539, 541, 545, 550, 554, 559, 561, 562, 564, 565, 570, 571, 572, 573, 575, 578, 579, 580, 585, 586, 594, 595, 598, 606, 607, 615, 619, 624, 625, 626, 627, 639, 641, 643, 645, 647, 650, 651, 653, 655, 659, 663, 664, 666, 668, 670, 672, 674, 676, 677, 680, 681, 683, 690, 691, 695, 700, 703, 704, 706, 709, 710, 713, 714, 718, 719, 721, 722, 723, 724, 725, 727, 728, 733, 734, 735, 736, 740, 741, 743, 747, 748, 750, 752, 756, 759, 761, 768, 773, 778, 780, 785, 786, 788, 792, 793, 796, 797, 801, 803, 805, 809, 811, 814, 815, 818, 822, 829, 832, 839, 842, 844, 846, 850, 854, 855, 856, 864, 868, 873, 882, 883, 888, 891, 898, 904, 905, 908, 909, 916, 919, 921, 925, 926, 928, 929, 930, 932, 938, 940, 941, 943, 947, 957, 961, 965, 966, 971, 975, 976, 977, 982, 983, 984, 987, 990, 994, 995, 997, 999} We remove these balls and are now left with, 265, balls The, 265, balls landed in the following cells [426, 481, 210, 486, 758, 296, 396, 728, 781, 690, 759, 951, 425, 720, 117, 49, 309, 606, 681, 407, 459, 770, 875, 979, 383, 373, 225, 990, 37, 162, 682, 607, 460, 94, 75, 915, 443, 180, 218, 905, 566, 542, 945, 10, 350, 655, 979, 616, 734, 39, 124, 923, 533, 336, 731, 483, 312, 550, 652, 461, 890, 858, 644, 844, 8, 915, 892, 83, 462, 576, 209, 855, 34, 825, 493, 599, 424, 904, 397, 557, 317, 100, 385, 512, 336, 848, 562, 504, 307, 200, 664, 212, 745, 396, 92, 799, 718, 559, 391, 466, 633, 27, 465, 445, 178, 162, 529, 421, 985, 463, 27, 526, 354, 173, 322, 665, 821, 629, 846, 276, 11, 504, 364, 26, 398, 373, 186, 924, 324, 326, 586, 756, 56, 320, 337, 429, 640, 169, 54, 46, 39, 153, 684, 942, 556, 307, 29, 734, 390, 534, 669, 661, 935, 82, 879, 57, 672, 593, 884, 321, 183, 371, 95, 456, 1000, 316, 422, 437, 41, 189, 803, 157, 104, 633, 553, 673, 873, 850, 582, 337, 577, 643, 329, 807, 606, 493, 837, 718, 1000, 261, 123, 42, 440, 595, 192, 555, 634, 626, 378, 619, 581, 82, 324, 119, 74, 26, 642, 124, 285, 832, 215, 772, 589, 496, 489, 885, 465, 516, 189, 696, 986, 431, 473, 696, 333, 509, 330, 733, 715, 544, 513, 59, 64, 575, 28, 247, 510, 876, 782, 805, 969, 134, 399, 202, 709, 224, 329, 815, 578, 718, 905, 438, 75, 101, 427, 139, 553, 96, 687, 664, 375, 428, 799, 849, 892] The set of cells that are occupied is {8, 10, 11, 26, 27, 28, 29, 34, 37, 39, 41, 42, 46, 49, 54, 56, 57, 59, 64, 74, 75, 82, 83, 92, 94, 95, 96, 100, 101, 104, 117, 119, 123, 124, 134, 139, 153, 157, 162, 169, 173, 178, 180, 183, 186, 189, 192, 200, 202, 209, 210, 212, 215, 218, 224, 225, 247, 261, 276, 285, 296, 307, 309, 312, 316, 317, 320, 321, 322, 324, 326, 329, 330, 333, 336, 337, 350, 354, 364, 371, 373, 375, 378, 383, 385, 390, 391, 396, 397, 398, 399, 407, 421, 422, 424, 425, 426, 427, 428, 429, 431, 437, 438, 440, 443, 445, 456, 459, 460, 461, 462, 463, 465, 466, 473, 481, 483, 486, 489, 493, 496, 504, 509, 510, 512, 513, 516, 526, 529, 533, 534, 542, 544, 550, 553, 555, 556, 557, 559, 562, 566, 575, 576, 577, 578, 581, 582, 586, 589, 593, 595, 599, 606, 607, 616, 619, 626, 629, 633, 634, 640, 642, 643, 644, 652, 655, 661, 664, 665, 669, 672, 673, 681, 682, 684, 687, 690, 696, 709, 715, 718, 720, 728, 731, 733, 734, 745, 756, 758, 759, 770, 772, 781, 782, 799, 803, 805, 807, 815, 821, 825, 832, 837, 844, 846, 848, 849, 850, 855, 858, 873, 875, 876, 879, 884, 885, 890, 892, 904, 905, 915, 923, 924, 935, 942, 945, 951, 969, 979, 985, 986, 990, 1000} The set of cells that have exactly one ball in them is {8, 10, 11, 28, 29, 34, 37, 41, 42, 46, 49, 54, 56, 57, 59, 64, 74, 83, 92, 94, 95, 96, 100, 101, 104, 117, 119, 123, 134, 139, 153, 157, 169, 173, 178, 180, 183, 186, 192, 200, 202, 209, 210, 212, 215, 218, 224, 225, 247, 261, 276, 285, 296, 309, 312, 316, 317, 320, 321, 322, 326, 330, 333, 350, 354, 364, 371, 375, 378, 383, 385, 390, 391, 397, 398, 399, 407, 421, 422, 424, 425, 426, 427, 428, 429, 431, 437, 438, 440, 443, 445, 456, 459, 460, 461, 462, 463, 466, 473, 481, 483, 486, 489, 496, 509, 510, 512, 513, 516, 526, 529, 533, 534, 542, 544, 550, 555, 556, 557, 559, 562, 566, 575, 576, 577, 578, 581, 582, 586, 589, 593, 595, 599, 607, 616, 619, 626, 629, 634, 640, 642, 643, 644, 652, 655, 661, 665, 669, 672, 673, 681, 682, 684, 687, 690, 709, 715, 720, 728, 731, 733, 745, 756, 758, 759, 770, 772, 781, 782, 803, 805, 807, 815, 821, 825, 832, 837, 844, 846, 848, 849, 850, 855, 858, 873, 875, 876, 879, 884, 885, 890, 904, 923, 924, 935, 942, 945, 951, 969, 985, 986, 990} We remove these balls and are now left with, 63, balls The, 63, balls landed in the following cells [600, 313, 943, 907, 268, 132, 693, 588, 570, 921, 290, 875, 955, 102, 745, 838, 945, 543, 71, 148, 970, 261, 601, 947, 997, 705, 818, 999, 961, 1, 714, 203, 171, 467, 295, 994, 477, 754, 220, 53, 996, 116, 688, 831, 3, 674, 486, 469, 685, 539, 145, 948, 587, 576, 115, 313, 911, 505, 570, 326, 731, 993, 946] The set of cells that are occupied is {1, 3, 53, 71, 102, 115, 116, 132, 145, 148, 171, 203, 220, 261, 268, 290, 295, 313, 326, 467, 469, 477, 486, 505, 539, 543, 570, 576, 587, 588, 600, 601, 674, 685, 688, 693, 705, 714, 731, 745, 754, 818, 831, 838, 875, 907, 911, 921, 943, 945, 946, 947, 948, 955, 961, 970, 993, 994, 996, 997, 999} The set of cells that have exactly one ball in them is {1, 3, 53, 71, 102, 115, 116, 132, 145, 148, 171, 203, 220, 261, 268, 290, 295, 326, 467, 469, 477, 486, 505, 539, 543, 576, 587, 588, 600, 601, 674, 685, 688, 693, 705, 714, 731, 745, 754, 818, 831, 838, 875, 907, 911, 921, 943, 945, 946, 947, 948, 955, 961, 970, 993, 994, 996, 997, 999} We remove these balls and are now left with, 4, balls The, 4, balls landed in the following cells [348, 927, 899, 278] The set of cells that are occupied is {278, 348, 899, 927} The set of cells that have exactly one ball in them is {278, 348, 899, 927} We remove these balls and are now left with, 0, balls This took, 5, rounds The, 1000, balls landed in the following cells [675, 575, 754, 343, 53, 960, 794, 598, 547, 775, 999, 958, 523, 941, 164, 610, 605, 648, 142, 57, 358, 661, 69, 48, 258, 11, 577, 799, 294, 844, 280, 387, 400, 195, 811, 361, 369, 847, 63, 473, 946, 363, 88, 225, 31, 721, 9, 620, 569, 731, 46, 798, 821, 948, 920, 658, 67, 689, 506, 266, 4, 817, 451, 577, 733, 892, 732, 954, 494, 359, 36, 12, 429, 628, 531, 37, 435, 937, 395, 207, 235, 270, 456, 148, 636, 62, 575, 370, 264, 330, 766, 483, 341, 402, 570, 80, 376, 754, 17, 239, 805, 511, 665, 990, 236, 738, 209, 113, 813, 248, 510, 202, 279, 837, 945, 147, 230, 522, 804, 589, 677, 774, 634, 556, 347, 558, 667, 64, 711, 847, 91, 277, 440, 274, 392, 677, 770, 653, 314, 642, 572, 637, 99, 992, 246, 317, 372, 129, 476, 396, 577, 566, 796, 893, 170, 61, 863, 391, 775, 691, 753, 673, 335, 845, 534, 973, 764, 262, 560, 547, 39, 209, 37, 30, 156, 84, 417, 604, 461, 57, 693, 532, 21, 340, 659, 798, 550, 94, 584, 504, 388, 920, 962, 145, 555, 815, 964, 966, 617, 343, 476, 925, 624, 496, 215, 750, 769, 414, 835, 380, 437, 351, 484, 381, 261, 295, 223, 657, 199, 143, 503, 99, 725, 74, 840, 100, 985, 88, 706, 882, 712, 289, 649, 949, 272, 963, 84, 231, 106, 241, 560, 454, 731, 688, 974, 896, 294, 199, 12, 456, 533, 281, 620, 296, 281, 674, 955, 808, 562, 770, 253, 183, 444, 842, 568, 128, 422, 362, 352, 89, 168, 106, 639, 60, 872, 265, 704, 984, 208, 220, 287, 751, 559, 810, 982, 735, 287, 66, 620, 67, 984, 392, 328, 191, 800, 231, 514, 660, 351, 119, 542, 861, 562, 897, 617, 295, 436, 771, 173, 852, 613, 558, 76, 862, 541, 728, 103, 673, 990, 348, 832, 696, 590, 876, 176, 567, 299, 370, 761, 877, 142, 394, 382, 85, 254, 417, 278, 360, 574, 265, 143, 98, 557, 737, 28, 287, 388, 830, 372, 276, 515, 509, 448, 961, 399, 201, 562, 306, 398, 219, 278, 253, 916, 226, 233, 984, 120, 427, 885, 92, 735, 166, 433, 391, 552, 204, 580, 647, 830, 888, 309, 455, 861, 575, 988, 69, 650, 784, 20, 466, 336, 134, 945, 18, 409, 298, 566, 993, 242, 205, 725, 498, 639, 200, 709, 534, 99, 386, 800, 978, 517, 709, 118, 98, 327, 759, 565, 343, 756, 516, 482, 197, 214, 846, 36, 232, 546, 98, 441, 457, 351, 60, 830, 288, 446, 593, 278, 329, 717, 103, 145, 235, 785, 94, 775, 956, 441, 991, 215, 66, 811, 143, 505, 656, 333, 210, 481, 324, 495, 567, 960, 772, 673, 604, 925, 581, 832, 625, 403, 881, 977, 474, 40, 824, 118, 347, 678, 588, 372, 438, 760, 590, 426, 359, 52, 176, 956, 590, 920, 140, 860, 707, 554, 986, 348, 69, 68, 374, 455, 196, 334, 645, 139, 963, 254, 318, 80, 616, 289, 737, 525, 792, 485, 563, 938, 569, 390, 206, 583, 738, 782, 492, 933, 221, 790, 384, 908, 112, 203, 497, 693, 116, 860, 501, 749, 420, 547, 721, 890, 520, 886, 33, 349, 305, 25, 272, 735, 481, 736, 261, 523, 845, 597, 615, 156, 779, 535, 64, 552, 770, 930, 52, 552, 422, 973, 766, 983, 273, 818, 144, 583, 375, 812, 705, 132, 206, 792, 785, 395, 687, 386, 514, 435, 918, 155, 19, 766, 824, 208, 773, 402, 435, 540, 995, 405, 481, 421, 574, 634, 483, 384, 213, 308, 406, 985, 552, 711, 980, 924, 25, 856, 784, 383, 668, 381, 801, 857, 774, 719, 675, 838, 542, 963, 709, 301, 998, 545, 384, 739, 678, 467, 208, 236, 330, 54, 652, 138, 55, 441, 143, 508, 634, 495, 258, 413, 638, 436, 22, 151, 290, 61, 142, 375, 322, 869, 360, 691, 216, 557, 379, 537, 454, 169, 823, 612, 319, 682, 338, 276, 191, 359, 517, 643, 263, 331, 172, 995, 741, 716, 684, 555, 599, 899, 644, 37, 602, 622, 704, 796, 485, 940, 714, 998, 994, 173, 606, 508, 266, 449, 584, 93, 117, 677, 414, 378, 414, 475, 653, 321, 746, 935, 678, 87, 963, 327, 513, 271, 117, 167, 354, 713, 500, 274, 135, 87, 519, 198, 246, 126, 54, 510, 619, 585, 973, 373, 178, 586, 94, 772, 651, 896, 330, 810, 673, 588, 372, 722, 565, 182, 34, 124, 945, 889, 575, 982, 974, 439, 225, 604, 14, 444, 720, 11, 822, 154, 873, 736, 776, 999, 714, 961, 30, 565, 643, 292, 503, 131, 948, 9, 733, 551, 286, 307, 264, 384, 653, 211, 699, 64, 372, 1000, 126, 639, 238, 511, 245, 113, 253, 798, 453, 799, 296, 123, 883, 502, 391, 707, 527, 259, 211, 481, 832, 435, 867, 775, 369, 836, 320, 331, 995, 134, 984, 408, 324, 372, 129, 199, 562, 345, 80, 519, 718, 760, 31, 464, 206, 743, 32, 99, 152, 784, 5, 660, 580, 99, 979, 362, 27, 134, 704, 825, 334, 274, 870, 112, 925, 782, 464, 575, 611, 619, 641, 594, 11, 963, 995, 671, 320, 453, 822, 784, 759, 396, 631, 336, 929, 775, 622, 721, 774, 147, 327, 62, 945, 88, 856, 685, 634, 384, 681, 397, 416, 450, 742, 187, 53, 298, 948, 404, 963, 606, 938, 406, 936, 573, 725, 304, 491, 218, 746, 215, 406, 117, 223, 139, 101, 795, 169, 283, 93, 608, 456, 325, 29, 916, 150, 366, 744, 415, 991, 527, 500, 508, 830, 255, 693, 917, 471, 285, 736, 702, 691, 343, 86, 348, 121, 179, 168, 629, 221, 294, 648, 714, 694, 847, 425, 893, 309, 611, 290, 842, 604, 848, 369, 557, 335, 166, 271, 501, 472, 120, 318, 286, 732, 211, 25, 131, 331, 41, 312, 659, 98, 839, 72, 592, 336, 219, 223, 408, 646, 768, 939, 989, 297, 153, 463, 893, 595, 58, 760] The set of cells that are occupied is {4, 5, 9, 11, 12, 14, 17, 18, 19, 20, 21, 22, 25, 27, 28, 29, 30, 31, 32, 33, 34, 36, 37, 39, 40, 41, 46, 48, 52, 53, 54, 55, 57, 58, 60, 61, 62, 63, 64, 66, 67, 68, 69, 72, 74, 76, 80, 84, 85, 86, 87, 88, 89, 91, 92, 93, 94, 98, 99, 100, 101, 103, 106, 112, 113, 116, 117, 118, 119, 120, 121, 123, 124, 126, 128, 129, 131, 132, 134, 135, 138, 139, 140, 142, 143, 144, 145, 147, 148, 150, 151, 152, 153, 154, 155, 156, 164, 166, 167, 168, 169, 170, 172, 173, 176, 178, 179, 182, 183, 187, 191, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 213, 214, 215, 216, 218, 219, 220, 221, 223, 225, 226, 230, 231, 232, 233, 235, 236, 238, 239, 241, 242, 245, 246, 248, 253, 254, 255, 258, 259, 261, 262, 263, 264, 265, 266, 270, 271, 272, 273, 274, 276, 277, 278, 279, 280, 281, 283, 285, 286, 287, 288, 289, 290, 292, 294, 295, 296, 297, 298, 299, 301, 304, 305, 306, 307, 308, 309, 312, 314, 317, 318, 319, 320, 321, 322, 324, 325, 327, 328, 329, 330, 331, 333, 334, 335, 336, 338, 340, 341, 343, 345, 347, 348, 349, 351, 352, 354, 358, 359, 360, 361, 362, 363, 366, 369, 370, 372, 373, 374, 375, 376, 378, 379, 380, 381, 382, 383, 384, 386, 387, 388, 390, 391, 392, 394, 395, 396, 397, 398, 399, 400, 402, 403, 404, 405, 406, 408, 409, 413, 414, 415, 416, 417, 420, 421, 422, 425, 426, 427, 429, 433, 435, 436, 437, 438, 439, 440, 441, 444, 446, 448, 449, 450, 451, 453, 454, 455, 456, 457, 461, 463, 464, 466, 467, 471, 472, 473, 474, 475, 476, 481, 482, 483, 484, 485, 491, 492, 494, 495, 496, 497, 498, 500, 501, 502, 503, 504, 505, 506, 508, 509, 510, 511, 513, 514, 515, 516, 517, 519, 520, 522, 523, 525, 527, 531, 532, 533, 534, 535, 537, 540, 541, 542, 545, 546, 547, 550, 551, 552, 554, 555, 556, 557, 558, 559, 560, 562, 563, 565, 566, 567, 568, 569, 570, 572, 573, 574, 575, 577, 580, 581, 583, 584, 585, 586, 588, 589, 590, 592, 593, 594, 595, 597, 598, 599, 602, 604, 605, 606, 608, 610, 611, 612, 613, 615, 616, 617, 619, 620, 622, 624, 625, 628, 629, 631, 634, 636, 637, 638, 639, 641, 642, 643, 644, 645, 646, 647, 648, 649, 650, 651, 652, 653, 656, 657, 658, 659, 660, 661, 665, 667, 668, 671, 673, 674, 675, 677, 678, 681, 682, 684, 685, 687, 688, 689, 691, 693, 694, 696, 699, 702, 704, 705, 706, 707, 709, 711, 712, 713, 714, 716, 717, 718, 719, 720, 721, 722, 725, 728, 731, 732, 733, 735, 736, 737, 738, 739, 741, 742, 743, 744, 746, 749, 750, 751, 753, 754, 756, 759, 760, 761, 764, 766, 768, 769, 770, 771, 772, 773, 774, 775, 776, 779, 782, 784, 785, 790, 792, 794, 795, 796, 798, 799, 800, 801, 804, 805, 808, 810, 811, 812, 813, 815, 817, 818, 821, 822, 823, 824, 825, 830, 832, 835, 836, 837, 838, 839, 840, 842, 844, 845, 846, 847, 848, 852, 856, 857, 860, 861, 862, 863, 867, 869, 870, 872, 873, 876, 877, 881, 882, 883, 885, 886, 888, 889, 890, 892, 893, 896, 897, 899, 908, 916, 917, 918, 920, 924, 925, 929, 930, 933, 935, 936, 937, 938, 939, 940, 941, 945, 946, 948, 949, 954, 955, 956, 958, 960, 961, 962, 963, 964, 966, 973, 974, 977, 978, 979, 980, 982, 983, 984, 985, 986, 988, 989, 990, 991, 992, 993, 994, 995, 998, 999, 1000} The set of cells that have exactly one ball in them is {4, 5, 14, 17, 18, 19, 20, 21, 22, 27, 28, 29, 32, 33, 34, 39, 40, 41, 46, 48, 55, 58, 63, 68, 72, 74, 76, 85, 86, 89, 91, 92, 100, 101, 116, 119, 121, 123, 124, 128, 132, 135, 138, 140, 144, 148, 150, 151, 152, 153, 154, 155, 164, 167, 170, 172, 178, 179, 182, 183, 187, 195, 196, 197, 198, 200, 201, 202, 203, 204, 205, 207, 210, 213, 214, 216, 218, 220, 226, 230, 232, 233, 238, 239, 241, 242, 245, 248, 255, 259, 262, 263, 270, 273, 277, 279, 280, 283, 285, 288, 292, 297, 299, 301, 304, 305, 306, 307, 308, 312, 314, 317, 319, 321, 322, 325, 328, 329, 333, 338, 340, 341, 345, 349, 352, 354, 358, 361, 363, 366, 373, 374, 376, 378, 379, 380, 382, 383, 387, 390, 394, 397, 398, 399, 400, 403, 404, 405, 409, 413, 415, 416, 420, 421, 425, 426, 427, 429, 433, 437, 438, 439, 440, 446, 448, 449, 450, 451, 457, 461, 463, 466, 467, 471, 472, 473, 474, 475, 482, 484, 491, 492, 494, 496, 497, 498, 502, 504, 505, 506, 509, 513, 515, 516, 520, 522, 525, 531, 532, 533, 535, 537, 540, 541, 545, 546, 550, 551, 554, 556, 559, 563, 568, 570, 572, 573, 581, 585, 586, 589, 592, 593, 594, 595, 597, 598, 599, 602, 605, 608, 610, 612, 613, 615, 616, 624, 625, 628, 629, 631, 636, 637, 638, 641, 642, 644, 645, 646, 647, 649, 650, 651, 652, 656, 657, 658, 661, 665, 667, 668, 671, 674, 681, 682, 684, 685, 687, 688, 689, 694, 696, 699, 702, 705, 706, 712, 713, 716, 717, 718, 719, 720, 722, 728, 739, 741, 742, 743, 744, 749, 750, 751, 753, 756, 761, 764, 768, 769, 771, 773, 776, 779, 790, 794, 795, 801, 804, 805, 808, 812, 813, 815, 817, 818, 821, 823, 825, 835, 836, 837, 838, 839, 840, 844, 846, 848, 852, 857, 862, 863, 867, 869, 870, 872, 873, 876, 877, 881, 882, 883, 885, 886, 888, 889, 890, 892, 897, 899, 908, 917, 918, 924, 929, 930, 933, 935, 936, 937, 939, 940, 941, 946, 949, 954, 955, 958, 962, 964, 966, 977, 978, 979, 980, 983, 986, 988, 989, 992, 993, 994, 1000} We remove these balls and are now left with, 619, balls The, 619, balls landed in the following cells [263, 240, 676, 878, 636, 592, 218, 6, 346, 985, 756, 372, 562, 911, 59, 817, 226, 484, 112, 322, 300, 812, 421, 598, 813, 35, 238, 683, 194, 835, 169, 326, 698, 709, 856, 373, 962, 847, 33, 329, 437, 767, 989, 772, 294, 543, 438, 244, 871, 121, 697, 980, 1000, 97, 606, 153, 826, 626, 4, 306, 511, 464, 311, 670, 764, 51, 34, 970, 466, 520, 724, 806, 448, 194, 131, 283, 430, 130, 203, 951, 948, 97, 616, 372, 515, 909, 551, 421, 293, 662, 748, 144, 760, 439, 378, 477, 487, 134, 543, 839, 146, 978, 465, 131, 526, 515, 927, 484, 857, 457, 142, 138, 860, 979, 495, 826, 953, 704, 388, 794, 196, 20, 100, 192, 387, 8, 596, 522, 985, 265, 783, 793, 972, 806, 257, 391, 694, 391, 521, 157, 91, 493, 36, 754, 566, 721, 579, 300, 219, 954, 12, 10, 467, 861, 87, 945, 483, 902, 485, 140, 816, 963, 14, 453, 559, 966, 683, 759, 485, 553, 919, 507, 650, 201, 277, 687, 559, 212, 444, 438, 386, 204, 940, 714, 825, 152, 163, 92, 437, 170, 609, 879, 437, 707, 949, 552, 935, 811, 991, 864, 523, 297, 587, 504, 685, 245, 768, 922, 590, 608, 934, 127, 227, 572, 499, 187, 367, 711, 145, 892, 636, 763, 877, 486, 165, 683, 498, 855, 507, 475, 192, 119, 319, 465, 850, 243, 794, 504, 610, 398, 794, 475, 566, 761, 231, 891, 374, 222, 264, 878, 937, 635, 817, 182, 325, 432, 704, 578, 237, 243, 527, 612, 369, 335, 321, 742, 891, 57, 989, 981, 149, 118, 886, 372, 747, 589, 128, 196, 549, 345, 404, 118, 661, 18, 15, 72, 321, 141, 704, 541, 370, 511, 394, 391, 58, 767, 482, 780, 345, 117, 796, 819, 405, 937, 339, 663, 144, 831, 890, 937, 929, 286, 249, 543, 414, 446, 336, 750, 73, 347, 899, 579, 38, 402, 953, 986, 101, 442, 263, 39, 427, 469, 387, 218, 973, 28, 945, 533, 739, 764, 573, 620, 196, 684, 534, 898, 322, 393, 928, 286, 552, 815, 87, 164, 814, 423, 626, 596, 211, 970, 28, 670, 524, 613, 405, 738, 919, 356, 167, 53, 579, 913, 161, 629, 261, 353, 451, 523, 142, 632, 419, 452, 51, 227, 355, 530, 516, 592, 460, 755, 604, 882, 678, 736, 710, 833, 375, 885, 457, 596, 38, 992, 43, 205, 999, 830, 220, 311, 639, 1000, 686, 320, 987, 519, 84, 985, 300, 355, 152, 179, 333, 755, 220, 145, 566, 222, 41, 382, 61, 566, 211, 574, 501, 762, 142, 905, 618, 339, 501, 584, 587, 690, 797, 990, 514, 585, 214, 889, 298, 129, 832, 749, 619, 95, 288, 643, 946, 39, 401, 40, 539, 76, 296, 192, 684, 254, 663, 81, 526, 304, 804, 5, 695, 375, 780, 322, 482, 481, 44, 599, 869, 183, 852, 321, 654, 488, 181, 398, 976, 46, 808, 829, 373, 131, 95, 36, 51, 845, 281, 977, 919, 355, 170, 909, 689, 879, 333, 579, 119, 964, 231, 502, 686, 188, 145, 822, 338, 160, 125, 216, 805, 1, 512, 884, 545, 869, 982, 623, 211, 243, 447, 841, 667, 425, 38, 954, 332, 457, 129, 87, 282, 395, 985, 967, 993, 380, 808, 968, 403, 784, 460, 644, 221, 757, 162, 565, 447, 477, 393, 405, 237, 632, 190, 293, 186, 297, 651, 137, 278, 765, 109, 422, 467, 599, 681, 157, 424, 846, 553, 262, 41, 452, 17, 20, 962, 842, 23, 377, 248, 265, 998, 713, 991, 864, 22, 615, 546, 169, 437, 622, 617, 653, 727, 199, 917, 664, 376, 822, 423, 764, 297, 439, 927, 851, 460, 325, 736, 349, 230] The set of cells that are occupied is {1, 4, 5, 6, 8, 10, 12, 14, 15, 17, 18, 20, 22, 23, 28, 33, 34, 35, 36, 38, 39, 40, 41, 43, 44, 46, 51, 53, 57, 58, 59, 61, 72, 73, 76, 81, 84, 87, 91, 92, 95, 97, 100, 101, 109, 112, 117, 118, 119, 121, 125, 127, 128, 129, 130, 131, 134, 137, 138, 140, 141, 142, 144, 145, 146, 149, 152, 153, 157, 160, 161, 162, 163, 164, 165, 167, 169, 170, 179, 181, 182, 183, 186, 187, 188, 190, 192, 194, 196, 199, 201, 203, 204, 205, 211, 212, 214, 216, 218, 219, 220, 221, 222, 226, 227, 230, 231, 237, 238, 240, 243, 244, 245, 248, 249, 254, 257, 261, 262, 263, 264, 265, 277, 278, 281, 282, 283, 286, 288, 293, 294, 296, 297, 298, 300, 304, 306, 311, 319, 320, 321, 322, 325, 326, 329, 332, 333, 335, 336, 338, 339, 345, 346, 347, 349, 353, 355, 356, 367, 369, 370, 372, 373, 374, 375, 376, 377, 378, 380, 382, 386, 387, 388, 391, 393, 394, 395, 398, 401, 402, 403, 404, 405, 414, 419, 421, 422, 423, 424, 425, 427, 430, 432, 437, 438, 439, 442, 444, 446, 447, 448, 451, 452, 453, 457, 460, 464, 465, 466, 467, 469, 475, 477, 481, 482, 483, 484, 485, 486, 487, 488, 493, 495, 498, 499, 501, 502, 504, 507, 511, 512, 514, 515, 516, 519, 520, 521, 522, 523, 524, 526, 527, 530, 533, 534, 539, 541, 543, 545, 546, 549, 551, 552, 553, 559, 562, 565, 566, 572, 573, 574, 578, 579, 584, 585, 587, 589, 590, 592, 596, 598, 599, 604, 606, 608, 609, 610, 612, 613, 615, 616, 617, 618, 619, 620, 622, 623, 626, 629, 632, 635, 636, 639, 643, 644, 650, 651, 653, 654, 661, 662, 663, 664, 667, 670, 676, 678, 681, 683, 684, 685, 686, 687, 689, 690, 694, 695, 697, 698, 704, 707, 709, 710, 711, 713, 714, 721, 724, 727, 736, 738, 739, 742, 747, 748, 749, 750, 754, 755, 756, 757, 759, 760, 761, 762, 763, 764, 765, 767, 768, 772, 780, 783, 784, 793, 794, 796, 797, 804, 805, 806, 808, 811, 812, 813, 814, 815, 816, 817, 819, 822, 825, 826, 829, 830, 831, 832, 833, 835, 839, 841, 842, 845, 846, 847, 850, 851, 852, 855, 856, 857, 860, 861, 864, 869, 871, 877, 878, 879, 882, 884, 885, 886, 889, 890, 891, 892, 898, 899, 902, 905, 909, 911, 913, 917, 919, 922, 927, 928, 929, 934, 935, 937, 940, 945, 946, 948, 949, 951, 953, 954, 962, 963, 964, 966, 967, 968, 970, 972, 973, 976, 977, 978, 979, 980, 981, 982, 985, 986, 987, 989, 990, 991, 992, 993, 998, 999, 1000} The set of cells that have exactly one ball in them is {1, 4, 5, 6, 8, 10, 12, 14, 15, 17, 18, 22, 23, 33, 34, 35, 40, 43, 44, 46, 53, 57, 58, 59, 61, 72, 73, 76, 81, 84, 91, 92, 100, 101, 109, 112, 117, 121, 125, 127, 128, 130, 134, 137, 138, 140, 141, 146, 149, 153, 160, 161, 162, 163, 164, 165, 167, 179, 181, 182, 183, 186, 187, 188, 190, 199, 201, 203, 204, 205, 212, 214, 216, 219, 221, 226, 230, 238, 240, 244, 245, 248, 249, 254, 257, 261, 262, 264, 277, 278, 281, 282, 283, 288, 294, 296, 298, 304, 306, 319, 320, 326, 329, 332, 335, 336, 338, 346, 347, 349, 353, 356, 367, 369, 370, 374, 376, 377, 378, 380, 382, 386, 388, 394, 395, 401, 402, 403, 404, 414, 419, 422, 424, 425, 427, 430, 432, 442, 444, 446, 448, 451, 453, 464, 466, 469, 481, 483, 486, 487, 488, 493, 495, 498, 499, 502, 512, 514, 516, 519, 520, 521, 522, 524, 527, 530, 533, 534, 539, 541, 545, 546, 549, 551, 562, 565, 572, 573, 574, 578, 584, 585, 589, 590, 598, 604, 606, 608, 609, 610, 612, 613, 615, 616, 617, 618, 619, 620, 622, 623, 629, 635, 639, 643, 644, 650, 651, 653, 654, 661, 662, 664, 667, 676, 678, 681, 685, 687, 689, 690, 694, 695, 697, 698, 707, 709, 710, 711, 713, 714, 721, 724, 727, 738, 739, 742, 747, 748, 749, 750, 754, 756, 757, 759, 760, 761, 762, 763, 765, 768, 772, 783, 784, 793, 796, 797, 804, 805, 811, 812, 813, 814, 815, 816, 819, 825, 829, 830, 831, 832, 833, 835, 839, 841, 842, 845, 846, 847, 850, 851, 852, 855, 856, 857, 860, 861, 871, 877, 882, 884, 885, 886, 889, 890, 892, 898, 899, 902, 905, 911, 913, 917, 922, 928, 929, 934, 935, 940, 946, 948, 949, 951, 963, 964, 966, 967, 968, 972, 973, 976, 977, 978, 979, 980, 981, 982, 986, 987, 990, 992, 993, 998, 999} We remove these balls and are now left with, 286, balls The, 286, balls landed in the following cells [366, 772, 768, 668, 958, 408, 452, 387, 858, 827, 741, 231, 545, 73, 588, 419, 94, 250, 605, 951, 444, 492, 591, 578, 297, 83, 475, 169, 297, 963, 382, 657, 689, 358, 184, 16, 765, 232, 989, 596, 624, 56, 922, 68, 620, 803, 409, 665, 310, 479, 968, 363, 344, 461, 186, 594, 993, 601, 640, 159, 973, 186, 756, 871, 632, 211, 943, 162, 236, 338, 679, 618, 659, 592, 958, 51, 661, 1000, 971, 899, 191, 302, 205, 208, 644, 628, 421, 824, 292, 975, 911, 477, 344, 863, 672, 271, 746, 551, 18, 133, 785, 960, 956, 537, 895, 87, 638, 609, 273, 366, 80, 354, 84, 255, 197, 831, 923, 616, 393, 52, 551, 50, 899, 726, 750, 503, 319, 552, 422, 961, 234, 29, 50, 909, 940, 681, 861, 661, 492, 177, 667, 736, 703, 633, 957, 731, 742, 520, 679, 881, 191, 432, 201, 176, 672, 527, 983, 20, 365, 598, 559, 438, 214, 964, 225, 579, 918, 649, 748, 508, 50, 750, 324, 829, 563, 695, 18, 945, 511, 29, 769, 212, 169, 987, 586, 465, 615, 30, 770, 824, 424, 910, 365, 342, 27, 497, 702, 323, 710, 888, 279, 775, 592, 836, 258, 22, 33, 151, 342, 623, 390, 323, 471, 893, 155, 299, 5, 306, 449, 376, 47, 301, 621, 185, 362, 642, 224, 675, 304, 680, 948, 403, 522, 249, 210, 295, 871, 904, 699, 737, 669, 528, 754, 591, 934, 136, 662, 316, 524, 650, 456, 853, 747, 297, 393, 674, 989, 105, 961, 451, 735, 517, 980, 774, 369, 834, 127, 970, 456, 819, 702, 456, 296, 990, 855, 410, 397, 747, 339, 160, 717, 794, 964, 839, 396, 568] The set of cells that are occupied is {5, 16, 18, 20, 22, 27, 29, 30, 33, 47, 50, 51, 52, 56, 68, 73, 80, 83, 84, 87, 94, 105, 127, 133, 136, 151, 155, 159, 160, 162, 169, 176, 177, 184, 185, 186, 191, 197, 201, 205, 208, 210, 211, 212, 214, 224, 225, 231, 232, 234, 236, 249, 250, 255, 258, 271, 273, 279, 292, 295, 296, 297, 299, 301, 302, 304, 306, 310, 316, 319, 323, 324, 338, 339, 342, 344, 354, 358, 362, 363, 365, 366, 369, 376, 382, 387, 390, 393, 396, 397, 403, 408, 409, 410, 419, 421, 422, 424, 432, 438, 444, 449, 451, 452, 456, 461, 465, 471, 475, 477, 479, 492, 497, 503, 508, 511, 517, 520, 522, 524, 527, 528, 537, 545, 551, 552, 559, 563, 568, 578, 579, 586, 588, 591, 592, 594, 596, 598, 601, 605, 609, 615, 616, 618, 620, 621, 623, 624, 628, 632, 633, 638, 640, 642, 644, 649, 650, 657, 659, 661, 662, 665, 667, 668, 669, 672, 674, 675, 679, 680, 681, 689, 695, 699, 702, 703, 710, 717, 726, 731, 735, 736, 737, 741, 742, 746, 747, 748, 750, 754, 756, 765, 768, 769, 770, 772, 774, 775, 785, 794, 803, 819, 824, 827, 829, 831, 834, 836, 839, 853, 855, 858, 861, 863, 871, 881, 888, 893, 895, 899, 904, 909, 910, 911, 918, 922, 923, 934, 940, 943, 945, 948, 951, 956, 957, 958, 960, 961, 963, 964, 968, 970, 971, 973, 975, 980, 983, 987, 989, 990, 993, 1000} The set of cells that have exactly one ball in them is {5, 16, 20, 22, 27, 30, 33, 47, 51, 52, 56, 68, 73, 80, 83, 84, 87, 94, 105, 127, 133, 136, 151, 155, 159, 160, 162, 176, 177, 184, 185, 197, 201, 205, 208, 210, 211, 212, 214, 224, 225, 231, 232, 234, 236, 249, 250, 255, 258, 271, 273, 279, 292, 295, 296, 299, 301, 302, 304, 306, 310, 316, 319, 324, 338, 339, 354, 358, 362, 363, 369, 376, 382, 387, 390, 396, 397, 403, 408, 409, 410, 419, 421, 422, 424, 432, 438, 444, 449, 451, 452, 461, 465, 471, 475, 477, 479, 497, 503, 508, 511, 517, 520, 522, 524, 527, 528, 537, 545, 552, 559, 563, 568, 578, 579, 586, 588, 594, 596, 598, 601, 605, 609, 615, 616, 618, 620, 621, 623, 624, 628, 632, 633, 638, 640, 642, 644, 649, 650, 657, 659, 662, 665, 667, 668, 669, 674, 675, 680, 681, 689, 695, 699, 703, 710, 717, 726, 731, 735, 736, 737, 741, 742, 746, 748, 754, 756, 765, 768, 769, 770, 772, 774, 775, 785, 794, 803, 819, 827, 829, 831, 834, 836, 839, 853, 855, 858, 861, 863, 881, 888, 893, 895, 904, 909, 910, 911, 918, 922, 923, 934, 940, 943, 945, 948, 951, 956, 957, 960, 963, 968, 970, 971, 973, 975, 980, 983, 987, 990, 993, 1000} We remove these balls and are now left with, 65, balls The, 65, balls landed in the following cells [281, 18, 808, 523, 852, 819, 567, 762, 625, 981, 891, 590, 828, 126, 326, 639, 249, 699, 998, 438, 637, 316, 77, 811, 338, 932, 89, 847, 557, 692, 176, 296, 629, 871, 974, 551, 846, 147, 486, 98, 422, 404, 853, 448, 966, 485, 36, 339, 749, 872, 865, 977, 656, 211, 671, 461, 24, 295, 80, 937, 823, 704, 618, 118, 395] The set of cells that are occupied is {18, 24, 36, 77, 80, 89, 98, 118, 126, 147, 176, 211, 249, 281, 295, 296, 316, 326, 338, 339, 395, 404, 422, 438, 448, 461, 485, 486, 523, 551, 557, 567, 590, 618, 625, 629, 637, 639, 656, 671, 692, 699, 704, 749, 762, 808, 811, 819, 823, 828, 846, 847, 852, 853, 865, 871, 872, 891, 932, 937, 966, 974, 977, 981, 998} The set of cells that have exactly one ball in them is {18, 24, 36, 77, 80, 89, 98, 118, 126, 147, 176, 211, 249, 281, 295, 296, 316, 326, 338, 339, 395, 404, 422, 438, 448, 461, 485, 486, 523, 551, 557, 567, 590, 618, 625, 629, 637, 639, 656, 671, 692, 699, 704, 749, 762, 808, 811, 819, 823, 828, 846, 847, 852, 853, 865, 871, 872, 891, 932, 937, 966, 974, 977, 981, 998} We remove these balls and are now left with, 0, balls This took, 4, rounds The, 1000, balls landed in the following cells [781, 309, 29, 154, 48, 385, 553, 963, 961, 58, 881, 186, 617, 585, 599, 295, 6, 787, 656, 839, 652, 756, 262, 530, 748, 596, 222, 470, 362, 121, 431, 333, 807, 30, 905, 881, 260, 375, 62, 924, 359, 621, 858, 319, 152, 697, 206, 199, 218, 987, 715, 408, 33, 621, 958, 743, 209, 859, 698, 857, 415, 774, 191, 315, 604, 270, 666, 636, 909, 83, 372, 776, 393, 51, 197, 144, 291, 417, 747, 445, 573, 134, 214, 358, 919, 279, 121, 784, 36, 158, 794, 647, 270, 313, 583, 481, 475, 868, 36, 935, 755, 118, 821, 418, 823, 441, 7, 806, 795, 557, 746, 122, 737, 819, 531, 283, 25, 330, 687, 707, 210, 372, 972, 79, 483, 895, 454, 677, 836, 157, 906, 342, 266, 893, 861, 549, 112, 732, 239, 634, 140, 702, 166, 470, 931, 933, 375, 820, 879, 279, 597, 465, 814, 219, 56, 561, 806, 306, 233, 173, 920, 128, 692, 163, 405, 548, 215, 384, 54, 722, 901, 506, 760, 532, 435, 497, 272, 367, 945, 146, 821, 864, 459, 672, 37, 470, 340, 161, 94, 889, 435, 811, 147, 3, 677, 96, 33, 130, 224, 568, 170, 742, 895, 770, 316, 286, 653, 983, 784, 676, 944, 329, 251, 947, 862, 120, 21, 609, 906, 720, 286, 249, 96, 432, 314, 872, 464, 14, 615, 670, 999, 557, 30, 67, 68, 379, 229, 977, 69, 288, 566, 493, 412, 858, 60, 822, 61, 677, 533, 31, 421, 371, 508, 630, 930, 635, 938, 668, 884, 5, 440, 180, 702, 144, 511, 34, 928, 210, 521, 495, 131, 237, 653, 329, 47, 123, 632, 584, 653, 323, 20, 732, 87, 973, 295, 753, 651, 780, 307, 215, 622, 104, 542, 417, 127, 564, 998, 425, 168, 910, 243, 686, 464, 342, 509, 262, 696, 364, 174, 373, 521, 987, 549, 740, 201, 88, 262, 628, 12, 987, 139, 128, 853, 685, 737, 625, 326, 791, 786, 731, 985, 58, 440, 696, 296, 554, 689, 317, 751, 23, 621, 399, 468, 646, 510, 208, 924, 863, 64, 44, 697, 415, 329, 800, 896, 947, 581, 196, 109, 439, 559, 106, 896, 928, 593, 11, 587, 294, 616, 879, 525, 547, 317, 636, 955, 179, 261, 993, 601, 93, 916, 417, 619, 730, 772, 756, 606, 133, 475, 31, 982, 220, 136, 787, 113, 409, 594, 276, 48, 503, 845, 558, 486, 832, 739, 233, 162, 128, 183, 531, 438, 585, 741, 885, 761, 110, 247, 756, 390, 423, 565, 596, 376, 121, 211, 417, 192, 524, 862, 117, 361, 983, 983, 482, 122, 491, 43, 848, 791, 223, 690, 803, 992, 885, 143, 663, 165, 533, 873, 931, 692, 149, 832, 658, 756, 692, 486, 577, 183, 811, 743, 777, 98, 634, 907, 7, 255, 91, 157, 252, 860, 548, 43, 307, 808, 543, 29, 710, 265, 477, 948, 526, 608, 930, 64, 819, 44, 444, 45, 119, 238, 180, 211, 462, 15, 759, 540, 503, 520, 535, 472, 629, 501, 118, 271, 666, 658, 306, 337, 203, 403, 558, 678, 995, 911, 225, 692, 62, 261, 997, 3, 49, 940, 181, 10, 970, 999, 884, 262, 876, 251, 483, 769, 925, 723, 736, 617, 563, 460, 558, 171, 148, 601, 292, 69, 492, 26, 75, 776, 242, 122, 562, 86, 378, 209, 659, 259, 738, 200, 713, 702, 412, 65, 315, 727, 93, 31, 510, 304, 620, 300, 642, 122, 718, 784, 852, 357, 548, 785, 148, 396, 192, 110, 230, 238, 603, 767, 943, 294, 935, 153, 136, 484, 496, 321, 913, 995, 710, 514, 988, 785, 703, 470, 919, 484, 407, 570, 725, 874, 262, 646, 334, 948, 709, 812, 661, 469, 852, 866, 348, 184, 241, 715, 166, 252, 33, 880, 697, 971, 412, 672, 783, 340, 311, 667, 271, 659, 935, 533, 684, 238, 6, 714, 471, 999, 964, 773, 237, 384, 224, 899, 569, 268, 167, 80, 55, 541, 729, 853, 924, 241, 166, 200, 156, 796, 605, 470, 131, 391, 81, 966, 544, 35, 192, 459, 336, 163, 348, 226, 782, 591, 521, 429, 417, 367, 764, 352, 931, 595, 226, 779, 623, 621, 5, 79, 17, 734, 634, 630, 204, 585, 861, 728, 769, 169, 886, 729, 427, 370, 56, 38, 923, 763, 910, 198, 507, 471, 616, 962, 642, 164, 915, 558, 157, 907, 578, 970, 115, 686, 599, 862, 622, 974, 82, 56, 574, 507, 210, 615, 384, 437, 875, 434, 345, 621, 656, 623, 889, 951, 306, 221, 899, 618, 978, 966, 5, 164, 345, 705, 160, 67, 558, 741, 138, 409, 735, 704, 944, 888, 473, 466, 89, 275, 67, 633, 58, 68, 775, 503, 980, 138, 303, 488, 475, 236, 742, 5, 820, 215, 223, 383, 264, 675, 679, 770, 337, 458, 74, 392, 195, 358, 214, 340, 14, 778, 633, 138, 513, 717, 594, 733, 114, 496, 608, 223, 684, 619, 36, 774, 44, 144, 186, 596, 217, 426, 593, 442, 702, 326, 1000, 709, 410, 170, 715, 484, 892, 572, 368, 354, 788, 644, 807, 104, 659, 725, 36, 643, 75, 992, 591, 99, 693, 556, 51, 516, 397, 843, 652, 631, 130, 47, 727, 332, 45, 764, 79, 385, 756, 136, 908, 948, 259, 938, 251, 548, 924, 898, 450, 824, 581, 604, 656, 808, 760, 817, 805, 909, 415, 758, 106, 483, 631, 311, 401, 703, 720, 49, 27, 367, 583, 765, 131, 35, 482, 175, 137, 148, 813, 333, 510, 711, 637, 428, 926, 888, 215, 333, 656, 330, 347, 541, 801, 517, 751, 421, 452, 55, 674, 794, 325, 506, 90, 758, 662, 502, 328, 937, 562, 985, 751, 533, 777, 669, 365, 340, 74, 727, 149, 399, 866, 647, 444, 409, 764, 170, 931, 541, 860, 736, 765, 708, 427, 213, 196, 368, 920, 195, 914, 930, 635, 100, 782, 180, 132, 189, 465, 880, 109, 127, 682, 255, 628, 550, 613, 4, 995, 124, 627, 24, 395, 19, 889, 598, 853, 227, 767, 276, 625, 341, 876] The set of cells that are occupied is {3, 4, 5, 6, 7, 10, 11, 12, 14, 15, 17, 19, 20, 21, 23, 24, 25, 26, 27, 29, 30, 31, 33, 34, 35, 36, 37, 38, 43, 44, 45, 47, 48, 49, 51, 54, 55, 56, 58, 60, 61, 62, 64, 65, 67, 68, 69, 74, 75, 79, 80, 81, 82, 83, 86, 87, 88, 89, 90, 91, 93, 94, 96, 98, 99, 100, 104, 106, 109, 110, 112, 113, 114, 115, 117, 118, 119, 120, 121, 122, 123, 124, 127, 128, 130, 131, 132, 133, 134, 136, 137, 138, 139, 140, 143, 144, 146, 147, 148, 149, 152, 153, 154, 156, 157, 158, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 173, 174, 175, 179, 180, 181, 183, 184, 186, 189, 191, 192, 195, 196, 197, 198, 199, 200, 201, 203, 204, 206, 208, 209, 210, 211, 213, 214, 215, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 229, 230, 233, 236, 237, 238, 239, 241, 242, 243, 247, 249, 251, 252, 255, 259, 260, 261, 262, 264, 265, 266, 268, 270, 271, 272, 275, 276, 279, 283, 286, 288, 291, 292, 294, 295, 296, 300, 303, 304, 306, 307, 309, 311, 313, 314, 315, 316, 317, 319, 321, 323, 325, 326, 328, 329, 330, 332, 333, 334, 336, 337, 340, 341, 342, 345, 347, 348, 352, 354, 357, 358, 359, 361, 362, 364, 365, 367, 368, 370, 371, 372, 373, 375, 376, 378, 379, 383, 384, 385, 390, 391, 392, 393, 395, 396, 397, 399, 401, 403, 405, 407, 408, 409, 410, 412, 415, 417, 418, 421, 423, 425, 426, 427, 428, 429, 431, 432, 434, 435, 437, 438, 439, 440, 441, 442, 444, 445, 450, 452, 454, 458, 459, 460, 462, 464, 465, 466, 468, 469, 470, 471, 472, 473, 475, 477, 481, 482, 483, 484, 486, 488, 491, 492, 493, 495, 496, 497, 501, 502, 503, 506, 507, 508, 509, 510, 511, 513, 514, 516, 517, 520, 521, 524, 525, 526, 530, 531, 532, 533, 535, 540, 541, 542, 543, 544, 547, 548, 549, 550, 553, 554, 556, 557, 558, 559, 561, 562, 563, 564, 565, 566, 568, 569, 570, 572, 573, 574, 577, 578, 581, 583, 584, 585, 587, 591, 593, 594, 595, 596, 597, 598, 599, 601, 603, 604, 605, 606, 608, 609, 613, 615, 616, 617, 618, 619, 620, 621, 622, 623, 625, 627, 628, 629, 630, 631, 632, 633, 634, 635, 636, 637, 642, 643, 644, 646, 647, 651, 652, 653, 656, 658, 659, 661, 662, 663, 666, 667, 668, 669, 670, 672, 674, 675, 676, 677, 678, 679, 682, 684, 685, 686, 687, 689, 690, 692, 693, 696, 697, 698, 702, 703, 704, 705, 707, 708, 709, 710, 711, 713, 714, 715, 717, 718, 720, 722, 723, 725, 727, 728, 729, 730, 731, 732, 733, 734, 735, 736, 737, 738, 739, 740, 741, 742, 743, 746, 747, 748, 751, 753, 755, 756, 758, 759, 760, 761, 763, 764, 765, 767, 769, 770, 772, 773, 774, 775, 776, 777, 778, 779, 780, 781, 782, 783, 784, 785, 786, 787, 788, 791, 794, 795, 796, 800, 801, 803, 805, 806, 807, 808, 811, 812, 813, 814, 817, 819, 820, 821, 822, 823, 824, 832, 836, 839, 843, 845, 848, 852, 853, 857, 858, 859, 860, 861, 862, 863, 864, 866, 868, 872, 873, 874, 875, 876, 879, 880, 881, 884, 885, 886, 888, 889, 892, 893, 895, 896, 898, 899, 901, 905, 906, 907, 908, 909, 910, 911, 913, 914, 915, 916, 919, 920, 923, 924, 925, 926, 928, 930, 931, 933, 935, 937, 938, 940, 943, 944, 945, 947, 948, 951, 955, 958, 961, 962, 963, 964, 966, 970, 971, 972, 973, 974, 977, 978, 980, 982, 983, 985, 987, 988, 992, 993, 995, 997, 998, 999, 1000} The set of cells that have exactly one ball in them is {4, 10, 11, 12, 15, 17, 19, 20, 21, 23, 24, 25, 26, 27, 34, 37, 38, 54, 60, 61, 65, 80, 81, 82, 83, 86, 87, 88, 89, 90, 91, 94, 98, 99, 100, 112, 113, 114, 115, 117, 119, 120, 123, 124, 132, 133, 134, 137, 139, 140, 143, 146, 147, 152, 153, 154, 156, 158, 160, 161, 162, 165, 167, 168, 169, 171, 173, 174, 175, 179, 181, 184, 189, 191, 197, 198, 199, 201, 203, 204, 206, 208, 213, 217, 218, 219, 220, 221, 222, 225, 227, 229, 230, 236, 239, 242, 243, 247, 249, 260, 264, 265, 266, 268, 272, 275, 283, 288, 291, 292, 296, 300, 303, 304, 309, 313, 314, 316, 319, 321, 323, 325, 328, 332, 334, 336, 341, 347, 352, 354, 357, 359, 361, 362, 364, 365, 370, 371, 373, 376, 378, 379, 383, 390, 391, 392, 393, 395, 396, 397, 401, 403, 405, 407, 408, 410, 418, 423, 425, 426, 428, 429, 431, 432, 434, 437, 438, 439, 441, 442, 445, 450, 452, 454, 458, 460, 462, 466, 468, 469, 472, 473, 477, 481, 488, 491, 492, 493, 495, 497, 501, 502, 508, 509, 511, 513, 514, 516, 517, 520, 524, 525, 526, 530, 532, 535, 540, 542, 543, 544, 547, 550, 553, 554, 556, 559, 561, 563, 564, 565, 566, 568, 569, 570, 572, 573, 574, 577, 578, 584, 587, 595, 597, 598, 603, 605, 606, 609, 613, 618, 620, 627, 629, 632, 637, 643, 644, 651, 661, 662, 663, 667, 668, 669, 670, 674, 675, 676, 678, 679, 682, 685, 687, 689, 690, 693, 698, 704, 705, 707, 708, 711, 713, 714, 717, 718, 722, 723, 728, 730, 731, 733, 734, 735, 738, 739, 740, 746, 747, 748, 753, 755, 759, 761, 763, 772, 773, 775, 778, 779, 780, 781, 783, 786, 788, 795, 796, 800, 801, 803, 805, 812, 813, 814, 817, 822, 823, 824, 836, 839, 843, 845, 848, 857, 859, 863, 864, 868, 872, 873, 874, 875, 886, 892, 893, 898, 901, 905, 908, 911, 913, 914, 915, 916, 923, 925, 926, 933, 937, 940, 943, 945, 951, 955, 958, 961, 962, 963, 964, 971, 972, 973, 974, 977, 978, 980, 982, 988, 993, 997, 998, 1000} We remove these balls and are now left with, 628, balls The, 628, balls landed in the following cells [594, 883, 698, 64, 812, 836, 194, 53, 294, 54, 125, 697, 336, 711, 386, 726, 746, 388, 791, 533, 44, 68, 604, 561, 889, 847, 429, 69, 224, 140, 562, 104, 183, 577, 610, 988, 159, 429, 36, 502, 474, 720, 48, 372, 600, 912, 747, 127, 878, 616, 929, 265, 391, 685, 544, 980, 215, 870, 157, 756, 40, 561, 394, 609, 269, 687, 845, 503, 777, 787, 83, 753, 37, 894, 202, 277, 864, 336, 716, 845, 360, 37, 798, 706, 535, 610, 691, 252, 238, 164, 389, 863, 397, 736, 824, 183, 513, 325, 316, 146, 85, 658, 204, 431, 996, 230, 396, 957, 136, 138, 927, 326, 835, 483, 204, 742, 50, 978, 739, 507, 728, 828, 115, 597, 90, 2, 119, 969, 746, 104, 101, 963, 279, 651, 858, 44, 887, 786, 332, 92, 471, 138, 23, 837, 399, 101, 752, 805, 855, 101, 628, 943, 457, 197, 34, 157, 292, 906, 7, 666, 178, 585, 610, 778, 18, 499, 225, 669, 917, 455, 456, 767, 18, 851, 987, 945, 82, 691, 800, 479, 953, 415, 973, 913, 634, 760, 411, 910, 983, 584, 598, 269, 51, 330, 94, 700, 176, 723, 889, 245, 273, 283, 865, 719, 995, 706, 315, 383, 577, 474, 737, 926, 833, 974, 763, 457, 509, 833, 614, 593, 32, 493, 120, 174, 174, 467, 300, 926, 585, 971, 845, 465, 5, 230, 611, 545, 602, 96, 964, 834, 640, 158, 564, 498, 354, 995, 753, 378, 769, 833, 491, 985, 81, 308, 161, 533, 559, 889, 886, 20, 745, 634, 186, 246, 584, 979, 244, 719, 975, 95, 720, 862, 253, 741, 763, 622, 859, 559, 402, 822, 495, 644, 908, 910, 355, 993, 209, 791, 466, 507, 781, 221, 476, 209, 670, 723, 556, 490, 421, 409, 333, 647, 878, 113, 824, 176, 772, 548, 969, 605, 190, 618, 338, 132, 898, 942, 482, 142, 107, 810, 427, 537, 607, 109, 433, 902, 314, 551, 918, 680, 101, 439, 466, 13, 586, 165, 618, 9, 938, 354, 257, 267, 509, 702, 77, 988, 438, 228, 437, 927, 827, 300, 433, 456, 521, 904, 404, 62, 793, 721, 949, 673, 234, 928, 560, 655, 631, 418, 67, 746, 779, 948, 742, 384, 75, 617, 69, 488, 526, 556, 930, 322, 874, 28, 304, 978, 566, 979, 124, 282, 617, 473, 120, 959, 382, 864, 391, 164, 710, 894, 554, 134, 782, 871, 401, 405, 530, 622, 415, 762, 679, 159, 226, 783, 888, 224, 580, 937, 563, 424, 269, 292, 588, 288, 810, 437, 434, 78, 716, 843, 542, 825, 630, 820, 75, 548, 245, 513, 268, 264, 538, 169, 331, 969, 120, 690, 308, 963, 267, 331, 589, 304, 532, 626, 448, 380, 431, 726, 675, 530, 959, 421, 860, 595, 928, 176, 866, 698, 681, 580, 572, 837, 200, 313, 507, 658, 50, 478, 371, 54, 682, 947, 576, 207, 545, 889, 494, 790, 413, 798, 860, 275, 670, 394, 503, 933, 639, 955, 541, 596, 636, 496, 262, 308, 330, 462, 1000, 76, 39, 518, 592, 840, 314, 979, 32, 242, 149, 48, 558, 104, 973, 373, 116, 633, 756, 909, 356, 837, 156, 41, 343, 28, 235, 309, 882, 703, 69, 424, 889, 791, 134, 395, 678, 765, 189, 504, 478, 202, 372, 220, 619, 932, 346, 357, 965, 756, 256, 616, 125, 397, 463, 391, 257, 763, 900, 216, 388, 816, 231, 78, 446, 575, 140, 87, 474, 719, 541, 185, 390, 757, 784, 422, 786, 918, 930, 71, 28, 669, 336, 160, 575, 211, 874, 930, 964, 957, 716, 738, 935, 335, 50, 72, 284, 724, 11, 67, 555, 876, 432, 469, 622, 884, 879, 289, 643, 3, 70, 799, 597, 480, 91, 104, 810, 336, 207, 184, 892, 862] The set of cells that are occupied is {2, 3, 5, 7, 9, 11, 13, 18, 20, 23, 28, 32, 34, 36, 37, 39, 40, 41, 44, 48, 50, 51, 53, 54, 62, 64, 67, 68, 69, 70, 71, 72, 75, 76, 77, 78, 81, 82, 83, 85, 87, 90, 91, 92, 94, 95, 96, 101, 104, 107, 109, 113, 115, 116, 119, 120, 124, 125, 127, 132, 134, 136, 138, 140, 142, 146, 149, 156, 157, 158, 159, 160, 161, 164, 165, 169, 174, 176, 178, 183, 184, 185, 186, 189, 190, 194, 197, 200, 202, 204, 207, 209, 211, 215, 216, 220, 221, 224, 225, 226, 228, 230, 231, 234, 235, 238, 242, 244, 245, 246, 252, 253, 256, 257, 262, 264, 265, 267, 268, 269, 273, 275, 277, 279, 282, 283, 284, 288, 289, 292, 294, 300, 304, 308, 309, 313, 314, 315, 316, 322, 325, 326, 330, 331, 332, 333, 335, 336, 338, 343, 346, 354, 355, 356, 357, 360, 371, 372, 373, 378, 380, 382, 383, 384, 386, 388, 389, 390, 391, 394, 395, 396, 397, 399, 401, 402, 404, 405, 409, 411, 413, 415, 418, 421, 422, 424, 427, 429, 431, 432, 433, 434, 437, 438, 439, 446, 448, 455, 456, 457, 462, 463, 465, 466, 467, 469, 471, 473, 474, 476, 478, 479, 480, 482, 483, 488, 490, 491, 493, 494, 495, 496, 498, 499, 502, 503, 504, 507, 509, 513, 518, 521, 526, 530, 532, 533, 535, 537, 538, 541, 542, 544, 545, 548, 551, 554, 555, 556, 558, 559, 560, 561, 562, 563, 564, 566, 572, 575, 576, 577, 580, 584, 585, 586, 588, 589, 592, 593, 594, 595, 596, 597, 598, 600, 602, 604, 605, 607, 609, 610, 611, 614, 616, 617, 618, 619, 622, 626, 628, 630, 631, 633, 634, 636, 639, 640, 643, 644, 647, 651, 655, 658, 666, 669, 670, 673, 675, 678, 679, 680, 681, 682, 685, 687, 690, 691, 697, 698, 700, 702, 703, 706, 710, 711, 716, 719, 720, 721, 723, 724, 726, 728, 736, 737, 738, 739, 741, 742, 745, 746, 747, 752, 753, 756, 757, 760, 762, 763, 765, 767, 769, 772, 777, 778, 779, 781, 782, 783, 784, 786, 787, 790, 791, 793, 798, 799, 800, 805, 810, 812, 816, 820, 822, 824, 825, 827, 828, 833, 834, 835, 836, 837, 840, 843, 845, 847, 851, 855, 858, 859, 860, 862, 863, 864, 865, 866, 870, 871, 874, 876, 878, 879, 882, 883, 884, 886, 887, 888, 889, 892, 894, 898, 900, 902, 904, 906, 908, 909, 910, 912, 913, 917, 918, 926, 927, 928, 929, 930, 932, 933, 935, 937, 938, 942, 943, 945, 947, 948, 949, 953, 955, 957, 959, 963, 964, 965, 969, 971, 973, 974, 975, 978, 979, 980, 983, 985, 987, 988, 993, 995, 996, 1000} The set of cells that have exactly one ball in them is {2, 3, 5, 7, 9, 11, 13, 20, 23, 34, 36, 39, 40, 41, 51, 53, 62, 64, 68, 70, 71, 72, 76, 77, 81, 82, 83, 85, 87, 90, 91, 92, 94, 95, 96, 107, 109, 113, 115, 116, 119, 124, 127, 132, 136, 142, 146, 149, 156, 158, 160, 161, 165, 169, 178, 184, 185, 186, 189, 190, 194, 197, 200, 211, 215, 216, 220, 221, 225, 226, 228, 231, 234, 235, 238, 242, 244, 246, 252, 253, 256, 262, 264, 265, 268, 273, 275, 277, 279, 282, 283, 284, 288, 289, 294, 309, 313, 315, 316, 322, 325, 326, 332, 333, 335, 338, 343, 346, 355, 356, 357, 360, 371, 373, 378, 380, 382, 383, 384, 386, 389, 390, 395, 396, 399, 401, 402, 404, 405, 409, 411, 413, 418, 422, 427, 432, 434, 438, 439, 446, 448, 455, 462, 463, 465, 467, 469, 471, 473, 476, 479, 480, 482, 483, 488, 490, 491, 493, 494, 495, 496, 498, 499, 502, 504, 518, 521, 526, 532, 535, 537, 538, 542, 544, 551, 554, 555, 558, 560, 562, 563, 564, 566, 572, 576, 586, 588, 589, 592, 593, 594, 595, 596, 598, 600, 602, 604, 605, 607, 609, 611, 614, 619, 626, 628, 630, 631, 633, 636, 639, 640, 643, 644, 647, 651, 655, 666, 673, 675, 678, 679, 680, 681, 682, 685, 687, 690, 697, 700, 702, 703, 710, 711, 721, 724, 728, 736, 737, 738, 739, 741, 745, 747, 752, 757, 760, 762, 765, 767, 769, 772, 777, 778, 779, 781, 782, 783, 784, 787, 790, 793, 799, 800, 805, 812, 816, 820, 822, 825, 827, 828, 834, 835, 836, 840, 843, 847, 851, 855, 858, 859, 863, 865, 866, 870, 871, 876, 879, 882, 883, 884, 886, 887, 888, 892, 898, 900, 902, 904, 906, 908, 909, 912, 913, 917, 929, 932, 933, 935, 937, 938, 942, 943, 945, 947, 948, 949, 953, 955, 965, 971, 974, 975, 980, 983, 985, 987, 993, 996, 1000} We remove these balls and are now left with, 298, balls The, 298, balls landed in the following cells [551, 425, 376, 862, 830, 571, 202, 604, 687, 947, 310, 857, 540, 581, 639, 437, 717, 280, 197, 712, 189, 919, 872, 800, 922, 757, 868, 946, 864, 870, 653, 282, 713, 512, 594, 287, 831, 801, 633, 174, 306, 866, 518, 351, 449, 692, 569, 231, 380, 8, 356, 250, 283, 449, 396, 912, 942, 954, 894, 712, 435, 499, 886, 449, 9, 824, 708, 586, 118, 317, 744, 529, 928, 731, 533, 963, 990, 86, 332, 996, 823, 437, 789, 124, 578, 185, 393, 932, 76, 647, 351, 687, 75, 669, 224, 709, 13, 71, 816, 457, 192, 581, 198, 663, 898, 561, 151, 465, 361, 793, 389, 141, 855, 192, 936, 589, 724, 796, 622, 641, 633, 319, 513, 407, 662, 480, 531, 396, 44, 19, 94, 49, 839, 86, 564, 197, 495, 600, 951, 332, 604, 403, 271, 666, 665, 928, 658, 325, 993, 265, 966, 486, 102, 365, 813, 462, 620, 715, 782, 394, 605, 247, 894, 500, 744, 576, 319, 690, 575, 653, 157, 750, 608, 978, 131, 887, 742, 350, 490, 316, 133, 905, 731, 525, 522, 240, 109, 727, 105, 39, 844, 961, 26, 528, 107, 636, 444, 420, 988, 156, 957, 38, 580, 477, 809, 466, 727, 895, 189, 91, 669, 760, 635, 244, 373, 379, 50, 931, 514, 698, 601, 764, 445, 98, 609, 598, 245, 952, 713, 726, 154, 360, 435, 759, 417, 451, 373, 812, 393, 594, 692, 576, 295, 874, 996, 854, 639, 493, 70, 848, 137, 34, 334, 842, 631, 276, 414, 15, 328, 163, 634, 509, 692, 440, 482, 328, 255, 382, 222, 385, 564, 412, 23, 351, 727, 916, 899, 552, 647, 680, 159, 241, 425, 192, 42, 339, 17, 749, 553, 242, 862, 443, 76, 8, 422, 895, 42, 679] The set of cells that are occupied is {8, 9, 13, 15, 17, 19, 23, 26, 34, 38, 39, 42, 44, 49, 50, 70, 71, 75, 76, 86, 91, 94, 98, 102, 105, 107, 109, 118, 124, 131, 133, 137, 141, 151, 154, 156, 157, 159, 163, 174, 185, 189, 192, 197, 198, 202, 222, 224, 231, 240, 241, 242, 244, 245, 247, 250, 255, 265, 271, 276, 280, 282, 283, 287, 295, 306, 310, 316, 317, 319, 325, 328, 332, 334, 339, 350, 351, 356, 360, 361, 365, 373, 376, 379, 380, 382, 385, 389, 393, 394, 396, 403, 407, 412, 414, 417, 420, 422, 425, 435, 437, 440, 443, 444, 445, 449, 451, 457, 462, 465, 466, 477, 480, 482, 486, 490, 493, 495, 499, 500, 509, 512, 513, 514, 518, 522, 525, 528, 529, 531, 533, 540, 551, 552, 553, 561, 564, 569, 571, 575, 576, 578, 580, 581, 586, 589, 594, 598, 600, 601, 604, 605, 608, 609, 620, 622, 631, 633, 634, 635, 636, 639, 641, 647, 653, 658, 662, 663, 665, 666, 669, 679, 680, 687, 690, 692, 698, 708, 709, 712, 713, 715, 717, 724, 726, 727, 731, 742, 744, 749, 750, 757, 759, 760, 764, 782, 789, 793, 796, 800, 801, 809, 812, 813, 816, 823, 824, 830, 831, 839, 842, 844, 848, 854, 855, 857, 862, 864, 866, 868, 870, 872, 874, 886, 887, 894, 895, 898, 899, 905, 912, 916, 919, 922, 928, 931, 932, 936, 942, 946, 947, 951, 952, 954, 957, 961, 963, 966, 978, 988, 990, 993, 996} The set of cells that have exactly one ball in them is {9, 13, 15, 17, 19, 23, 26, 34, 38, 39, 44, 49, 50, 70, 71, 75, 91, 94, 98, 102, 105, 107, 109, 118, 124, 131, 133, 137, 141, 151, 154, 156, 157, 159, 163, 174, 185, 198, 202, 222, 224, 231, 240, 241, 242, 244, 245, 247, 250, 255, 265, 271, 276, 280, 282, 283, 287, 295, 306, 310, 316, 317, 325, 334, 339, 350, 356, 360, 361, 365, 376, 379, 380, 382, 385, 389, 394, 403, 407, 412, 414, 417, 420, 422, 440, 443, 444, 445, 451, 457, 462, 465, 466, 477, 480, 482, 486, 490, 493, 495, 499, 500, 509, 512, 513, 514, 518, 522, 525, 528, 529, 531, 533, 540, 551, 552, 553, 561, 569, 571, 575, 578, 580, 586, 589, 598, 600, 601, 605, 608, 609, 620, 622, 631, 634, 635, 636, 641, 658, 662, 663, 665, 666, 679, 680, 690, 698, 708, 709, 715, 717, 724, 726, 742, 749, 750, 757, 759, 760, 764, 782, 789, 793, 796, 800, 801, 809, 812, 813, 816, 823, 824, 830, 831, 839, 842, 844, 848, 854, 855, 857, 864, 866, 868, 870, 872, 874, 886, 887, 898, 899, 905, 912, 916, 919, 922, 931, 932, 936, 942, 946, 947, 951, 952, 954, 957, 961, 963, 966, 978, 988, 990, 993} We remove these balls and are now left with, 85, balls The, 85, balls landed in the following cells [97, 983, 867, 717, 905, 396, 382, 446, 983, 392, 705, 29, 38, 913, 75, 438, 391, 44, 788, 151, 608, 654, 442, 862, 635, 874, 783, 185, 957, 713, 711, 571, 940, 249, 219, 527, 964, 144, 958, 769, 566, 7, 911, 169, 865, 378, 607, 369, 238, 569, 152, 597, 525, 470, 435, 602, 311, 110, 178, 574, 650, 945, 368, 574, 790, 352, 784, 482, 925, 848, 97, 170, 751, 852, 197, 595, 478, 556, 599, 195, 655, 30, 796, 352, 670] The set of cells that are occupied is {7, 29, 30, 38, 44, 75, 97, 110, 144, 151, 152, 169, 170, 178, 185, 195, 197, 219, 238, 249, 311, 352, 368, 369, 378, 382, 391, 392, 396, 435, 438, 442, 446, 470, 478, 482, 525, 527, 556, 566, 569, 571, 574, 595, 597, 599, 602, 607, 608, 635, 650, 654, 655, 670, 705, 711, 713, 717, 751, 769, 783, 784, 788, 790, 796, 848, 852, 862, 865, 867, 874, 905, 911, 913, 925, 940, 945, 957, 958, 964, 983} The set of cells that have exactly one ball in them is {7, 29, 30, 38, 44, 75, 110, 144, 151, 152, 169, 170, 178, 185, 195, 197, 219, 238, 249, 311, 368, 369, 378, 382, 391, 392, 396, 435, 438, 442, 446, 470, 478, 482, 525, 527, 556, 566, 569, 571, 595, 597, 599, 602, 607, 608, 635, 650, 654, 655, 670, 705, 711, 713, 717, 751, 769, 783, 784, 788, 790, 796, 848, 852, 862, 865, 867, 874, 905, 911, 913, 925, 940, 945, 957, 958, 964} We remove these balls and are now left with, 8, balls The, 8, balls landed in the following cells [42, 406, 450, 291, 576, 581, 272, 640] The set of cells that are occupied is {42, 272, 291, 406, 450, 576, 581, 640} The set of cells that have exactly one ball in them is {42, 272, 291, 406, 450, 576, 581, 640} We remove these balls and are now left with, 0, balls This took, 5, rounds The, 1000, balls landed in the following cells [16, 748, 989, 201, 385, 753, 474, 240, 459, 117, 716, 313, 613, 230, 326, 77, 783, 915, 733, 395, 703, 781, 957, 4, 409, 574, 240, 920, 662, 889, 59, 533, 789, 916, 549, 337, 40, 933, 809, 791, 988, 995, 441, 836, 882, 926, 472, 313, 545, 350, 526, 987, 525, 225, 883, 292, 812, 150, 114, 700, 487, 847, 447, 168, 677, 256, 270, 816, 138, 803, 804, 655, 968, 322, 108, 739, 59, 154, 891, 673, 789, 878, 899, 578, 586, 340, 525, 868, 743, 953, 203, 649, 383, 3, 677, 227, 888, 628, 675, 24, 938, 214, 619, 911, 928, 449, 455, 32, 745, 115, 827, 814, 52, 554, 591, 504, 898, 198, 34, 550, 762, 610, 104, 819, 21, 852, 914, 419, 743, 246, 203, 860, 934, 880, 431, 237, 111, 396, 267, 924, 150, 578, 924, 447, 883, 177, 80, 566, 67, 301, 528, 531, 98, 294, 763, 750, 716, 575, 266, 382, 673, 585, 12, 922, 726, 493, 13, 736, 503, 253, 330, 180, 597, 717, 723, 262, 709, 279, 279, 86, 691, 907, 390, 22, 760, 595, 305, 268, 293, 183, 276, 195, 772, 280, 273, 784, 449, 864, 242, 15, 162, 679, 523, 710, 693, 416, 761, 83, 949, 27, 551, 712, 834, 953, 827, 260, 641, 67, 55, 338, 198, 95, 863, 276, 887, 366, 710, 291, 501, 978, 786, 85, 955, 29, 784, 665, 402, 6, 487, 970, 93, 837, 651, 141, 871, 745, 967, 860, 433, 953, 354, 600, 415, 450, 531, 744, 730, 332, 232, 974, 189, 339, 1000, 447, 693, 941, 861, 998, 874, 363, 758, 282, 892, 234, 945, 552, 505, 670, 776, 903, 821, 427, 578, 26, 932, 736, 123, 502, 406, 139, 108, 931, 626, 426, 857, 618, 746, 177, 915, 176, 311, 288, 554, 888, 763, 534, 699, 931, 144, 134, 43, 669, 442, 719, 997, 717, 168, 367, 738, 71, 805, 497, 393, 428, 689, 741, 222, 636, 953, 152, 463, 495, 735, 512, 986, 910, 301, 784, 285, 683, 810, 43, 475, 23, 857, 543, 728, 800, 504, 120, 81, 342, 16, 231, 444, 272, 110, 986, 968, 549, 918, 454, 855, 639, 243, 348, 848, 974, 821, 560, 101, 236, 875, 790, 817, 792, 869, 827, 735, 490, 78, 136, 72, 291, 93, 939, 800, 644, 645, 683, 677, 816, 897, 377, 406, 539, 573, 632, 769, 155, 620, 511, 707, 206, 71, 963, 574, 79, 786, 204, 656, 555, 725, 32, 115, 511, 243, 968, 236, 545, 558, 265, 432, 968, 161, 727, 656, 30, 239, 401, 251, 952, 229, 600, 818, 461, 285, 991, 422, 864, 182, 715, 705, 539, 865, 832, 83, 407, 228, 648, 882, 472, 60, 572, 13, 328, 987, 368, 963, 927, 300, 128, 704, 824, 609, 23, 203, 435, 907, 897, 509, 431, 468, 350, 77, 577, 906, 67, 529, 165, 648, 576, 374, 912, 993, 599, 341, 839, 849, 803, 839, 204, 346, 102, 488, 125, 749, 130, 982, 338, 322, 45, 780, 198, 980, 425, 803, 749, 645, 967, 742, 384, 789, 111, 988, 211, 926, 796, 557, 214, 232, 38, 429, 1, 984, 735, 307, 287, 324, 177, 849, 364, 950, 438, 861, 476, 298, 369, 897, 886, 288, 342, 23, 609, 137, 38, 482, 777, 636, 403, 323, 238, 851, 439, 28, 302, 823, 646, 316, 366, 581, 686, 759, 915, 303, 338, 487, 13, 772, 2, 436, 786, 468, 41, 289, 290, 799, 704, 59, 942, 891, 638, 418, 838, 322, 891, 951, 150, 116, 942, 327, 381, 617, 679, 574, 515, 395, 976, 409, 792, 860, 601, 397, 726, 158, 365, 816, 223, 230, 841, 158, 705, 726, 679, 936, 451, 285, 378, 232, 604, 602, 205, 153, 845, 134, 271, 843, 811, 839, 487, 293, 227, 534, 995, 136, 875, 403, 779, 495, 720, 170, 771, 761, 606, 367, 562, 74, 387, 815, 688, 47, 640, 416, 143, 821, 722, 816, 890, 162, 963, 866, 483, 837, 363, 434, 628, 864, 164, 658, 75, 253, 523, 426, 285, 568, 530, 620, 951, 741, 921, 81, 695, 333, 732, 663, 252, 136, 268, 946, 820, 392, 270, 296, 431, 738, 442, 959, 30, 674, 87, 284, 252, 675, 160, 537, 368, 65, 375, 938, 630, 110, 592, 45, 512, 846, 13, 778, 807, 315, 104, 3, 711, 487, 282, 372, 526, 658, 953, 810, 52, 557, 645, 905, 451, 123, 212, 912, 828, 16, 496, 770, 26, 373, 181, 28, 429, 73, 288, 954, 584, 51, 338, 979, 194, 858, 465, 864, 274, 110, 230, 851, 899, 152, 103, 303, 425, 967, 130, 336, 329, 776, 509, 500, 702, 465, 87, 6, 159, 766, 235, 611, 991, 519, 954, 342, 452, 611, 405, 677, 209, 128, 688, 156, 534, 291, 778, 612, 924, 551, 521, 602, 249, 193, 694, 90, 29, 601, 515, 106, 474, 848, 472, 433, 775, 910, 112, 258, 786, 137, 523, 738, 646, 941, 60, 32, 310, 292, 447, 140, 212, 530, 572, 214, 848, 595, 825, 906, 921, 313, 477, 6, 839, 252, 568, 42, 777, 144, 470, 739, 741, 552, 55, 386, 293, 166, 410, 70, 221, 934, 915, 202, 278, 237, 238, 487, 387, 227, 202, 984, 934, 798, 451, 491, 902, 192, 370, 50, 191, 516, 557, 61, 361, 803, 766, 829, 29, 436, 991, 226, 642, 206, 52, 320, 78, 455, 301, 268, 340, 311, 290, 91, 547, 314, 926, 255, 48, 217, 409, 92, 260, 881, 561, 827, 997, 524, 90, 450, 202, 376, 716, 593, 640, 543, 879, 750, 183, 188, 691, 152, 457, 618, 15, 816, 141, 31, 332, 187, 824, 696, 310, 161, 711, 854, 491, 715, 910, 588, 726, 504, 984, 663, 156, 756, 708, 832, 20, 455, 174, 598, 717, 705, 329, 452, 786, 694, 408, 63, 377, 548, 27, 384, 93, 125, 352, 671, 374, 698, 773, 377, 8, 898, 888, 844, 123, 188, 582, 326, 583, 627, 375, 561, 645, 903, 694, 215, 68, 816, 662, 819, 527] The set of cells that are occupied is {1, 2, 3, 4, 6, 8, 12, 13, 15, 16, 20, 21, 22, 23, 24, 26, 27, 28, 29, 30, 31, 32, 34, 38, 40, 41, 42, 43, 45, 47, 48, 50, 51, 52, 55, 59, 60, 61, 63, 65, 67, 68, 70, 71, 72, 73, 74, 75, 77, 78, 79, 80, 81, 83, 85, 86, 87, 90, 91, 92, 93, 95, 98, 101, 102, 103, 104, 106, 108, 110, 111, 112, 114, 115, 116, 117, 120, 123, 125, 128, 130, 134, 136, 137, 138, 139, 140, 141, 143, 144, 150, 152, 153, 154, 155, 156, 158, 159, 160, 161, 162, 164, 165, 166, 168, 170, 174, 176, 177, 180, 181, 182, 183, 187, 188, 189, 191, 192, 193, 194, 195, 198, 201, 202, 203, 204, 205, 206, 209, 211, 212, 214, 215, 217, 221, 222, 223, 225, 226, 227, 228, 229, 230, 231, 232, 234, 235, 236, 237, 238, 239, 240, 242, 243, 246, 249, 251, 252, 253, 255, 256, 258, 260, 262, 265, 266, 267, 268, 270, 271, 272, 273, 274, 276, 278, 279, 280, 282, 284, 285, 287, 288, 289, 290, 291, 292, 293, 294, 296, 298, 300, 301, 302, 303, 305, 307, 310, 311, 313, 314, 315, 316, 320, 322, 323, 324, 326, 327, 328, 329, 330, 332, 333, 336, 337, 338, 339, 340, 341, 342, 346, 348, 350, 352, 354, 361, 363, 364, 365, 366, 367, 368, 369, 370, 372, 373, 374, 375, 376, 377, 378, 381, 382, 383, 384, 385, 386, 387, 390, 392, 393, 395, 396, 397, 401, 402, 403, 405, 406, 407, 408, 409, 410, 415, 416, 418, 419, 422, 425, 426, 427, 428, 429, 431, 432, 433, 434, 435, 436, 438, 439, 441, 442, 444, 447, 449, 450, 451, 452, 454, 455, 457, 459, 461, 463, 465, 468, 470, 472, 474, 475, 476, 477, 482, 483, 487, 488, 490, 491, 493, 495, 496, 497, 500, 501, 502, 503, 504, 505, 509, 511, 512, 515, 516, 519, 521, 523, 524, 525, 526, 527, 528, 529, 530, 531, 533, 534, 537, 539, 543, 545, 547, 548, 549, 550, 551, 552, 554, 555, 557, 558, 560, 561, 562, 566, 568, 572, 573, 574, 575, 576, 577, 578, 581, 582, 583, 584, 585, 586, 588, 591, 592, 593, 595, 597, 598, 599, 600, 601, 602, 604, 606, 609, 610, 611, 612, 613, 617, 618, 619, 620, 626, 627, 628, 630, 632, 636, 638, 639, 640, 641, 642, 644, 645, 646, 648, 649, 651, 655, 656, 658, 662, 663, 665, 669, 670, 671, 673, 674, 675, 677, 679, 683, 686, 688, 689, 691, 693, 694, 695, 696, 698, 699, 700, 702, 703, 704, 705, 707, 708, 709, 710, 711, 712, 715, 716, 717, 719, 720, 722, 723, 725, 726, 727, 728, 730, 732, 733, 735, 736, 738, 739, 741, 742, 743, 744, 745, 746, 748, 749, 750, 753, 756, 758, 759, 760, 761, 762, 763, 766, 769, 770, 771, 772, 773, 775, 776, 777, 778, 779, 780, 781, 783, 784, 786, 789, 790, 791, 792, 796, 798, 799, 800, 803, 804, 805, 807, 809, 810, 811, 812, 814, 815, 816, 817, 818, 819, 820, 821, 823, 824, 825, 827, 828, 829, 832, 834, 836, 837, 838, 839, 841, 843, 844, 845, 846, 847, 848, 849, 851, 852, 854, 855, 857, 858, 860, 861, 863, 864, 865, 866, 868, 869, 871, 874, 875, 878, 879, 880, 881, 882, 883, 886, 887, 888, 889, 890, 891, 892, 897, 898, 899, 902, 903, 905, 906, 907, 910, 911, 912, 914, 915, 916, 918, 920, 921, 922, 924, 926, 927, 928, 931, 932, 933, 934, 936, 938, 939, 941, 942, 945, 946, 949, 950, 951, 952, 953, 954, 955, 957, 959, 963, 967, 968, 970, 974, 976, 978, 979, 980, 982, 984, 986, 987, 988, 989, 991, 993, 995, 997, 998, 1000} The set of cells that have exactly one ball in them is {1, 2, 4, 8, 12, 20, 21, 22, 24, 31, 34, 40, 41, 42, 47, 48, 50, 51, 61, 63, 65, 68, 70, 72, 73, 74, 75, 79, 80, 85, 86, 91, 92, 95, 98, 101, 102, 103, 106, 112, 114, 116, 117, 120, 138, 139, 140, 143, 153, 154, 155, 159, 160, 164, 165, 166, 170, 174, 176, 180, 181, 182, 187, 189, 191, 192, 193, 194, 195, 201, 205, 209, 211, 215, 217, 221, 222, 223, 225, 226, 228, 229, 231, 234, 235, 239, 242, 246, 249, 251, 255, 256, 258, 262, 265, 266, 267, 271, 272, 273, 274, 278, 280, 284, 287, 289, 294, 296, 298, 300, 302, 305, 307, 314, 315, 316, 320, 323, 324, 327, 328, 330, 333, 336, 337, 339, 341, 346, 348, 352, 354, 361, 364, 365, 369, 370, 372, 373, 376, 378, 381, 382, 383, 385, 386, 390, 392, 393, 396, 397, 401, 402, 405, 407, 408, 410, 415, 418, 419, 422, 427, 428, 432, 434, 435, 438, 439, 441, 444, 454, 457, 459, 461, 463, 470, 475, 476, 477, 482, 483, 488, 490, 493, 496, 497, 500, 501, 502, 503, 505, 516, 519, 521, 524, 527, 528, 529, 533, 537, 547, 548, 550, 555, 558, 560, 562, 566, 573, 575, 576, 577, 581, 582, 583, 584, 585, 586, 588, 591, 592, 593, 597, 598, 599, 604, 606, 610, 612, 613, 617, 619, 626, 627, 630, 632, 638, 639, 641, 642, 644, 649, 651, 655, 665, 669, 670, 671, 674, 686, 689, 695, 696, 698, 699, 700, 702, 703, 707, 708, 709, 712, 719, 720, 722, 723, 725, 727, 728, 730, 732, 733, 742, 744, 746, 748, 753, 756, 758, 759, 760, 762, 769, 770, 771, 773, 775, 779, 780, 781, 783, 790, 791, 796, 798, 799, 804, 805, 807, 809, 811, 812, 814, 815, 817, 818, 820, 823, 825, 828, 829, 834, 836, 838, 841, 843, 844, 845, 846, 847, 852, 854, 855, 858, 863, 865, 866, 868, 869, 871, 874, 878, 879, 880, 881, 886, 887, 889, 890, 892, 902, 905, 911, 914, 916, 918, 920, 922, 927, 928, 932, 933, 936, 939, 945, 946, 949, 950, 952, 955, 957, 959, 970, 976, 978, 979, 980, 982, 989, 993, 998, 1000} We remove these balls and are now left with, 629, balls The, 629, balls landed in the following cells [345, 71, 648, 468, 889, 970, 262, 460, 78, 345, 602, 81, 761, 998, 588, 734, 604, 408, 100, 311, 503, 220, 308, 701, 783, 630, 925, 378, 603, 529, 98, 551, 452, 582, 334, 918, 731, 145, 148, 691, 766, 459, 531, 118, 604, 303, 286, 953, 809, 86, 662, 739, 985, 291, 609, 12, 201, 468, 793, 982, 411, 766, 58, 766, 326, 49, 409, 607, 283, 466, 918, 237, 912, 860, 666, 744, 52, 170, 1000, 809, 742, 483, 605, 25, 631, 962, 376, 264, 862, 875, 125, 763, 146, 72, 57, 598, 346, 648, 542, 607, 772, 866, 173, 220, 881, 517, 431, 30, 744, 188, 920, 962, 38, 309, 69, 601, 463, 885, 491, 372, 488, 954, 816, 943, 290, 642, 648, 7, 209, 445, 1000, 594, 236, 345, 754, 474, 669, 849, 669, 42, 781, 511, 274, 367, 349, 530, 893, 814, 686, 181, 807, 681, 357, 253, 328, 970, 65, 39, 249, 580, 645, 167, 322, 343, 95, 217, 886, 145, 953, 376, 188, 593, 796, 327, 741, 206, 458, 812, 931, 433, 872, 94, 185, 595, 688, 225, 729, 58, 328, 376, 701, 853, 750, 562, 70, 482, 577, 870, 197, 391, 641, 46, 329, 778, 177, 509, 529, 755, 479, 152, 8, 374, 106, 756, 445, 943, 416, 973, 599, 29, 576, 142, 706, 396, 293, 646, 34, 825, 129, 252, 453, 56, 83, 191, 757, 119, 959, 533, 461, 504, 211, 79, 569, 898, 169, 387, 978, 622, 280, 275, 97, 729, 660, 746, 107, 329, 202, 506, 803, 78, 902, 456, 644, 121, 243, 532, 1000, 788, 553, 469, 809, 761, 521, 627, 607, 539, 138, 166, 721, 645, 156, 691, 13, 228, 17, 51, 355, 735, 930, 637, 952, 778, 899, 322, 741, 833, 418, 63, 498, 767, 415, 639, 42, 538, 922, 723, 189, 540, 535, 738, 854, 546, 821, 373, 847, 895, 382, 560, 936, 528, 370, 385, 282, 80, 786, 675, 342, 373, 105, 812, 474, 771, 156, 852, 444, 249, 288, 340, 912, 354, 637, 223, 694, 831, 370, 778, 35, 730, 20, 487, 865, 40, 76, 356, 869, 497, 326, 163, 916, 170, 662, 123, 95, 202, 806, 91, 112, 173, 147, 328, 232, 528, 210, 703, 569, 203, 292, 12, 809, 213, 56, 655, 239, 664, 907, 607, 542, 846, 51, 960, 857, 852, 764, 914, 211, 445, 17, 683, 394, 640, 212, 815, 680, 317, 57, 114, 102, 774, 8, 167, 651, 971, 772, 449, 780, 404, 353, 911, 382, 414, 155, 727, 797, 98, 90, 257, 662, 374, 189, 610, 285, 956, 481, 134, 860, 819, 472, 133, 656, 124, 391, 258, 977, 73, 632, 805, 50, 214, 413, 597, 398, 103, 946, 315, 168, 671, 145, 901, 370, 263, 502, 785, 490, 782, 360, 193, 197, 947, 365, 427, 179, 780, 971, 879, 809, 673, 904, 332, 436, 564, 552, 535, 299, 423, 220, 90, 691, 138, 261, 977, 188, 662, 460, 108, 110, 543, 617, 3, 608, 232, 741, 550, 491, 918, 912, 306, 917, 339, 611, 248, 548, 553, 198, 741, 481, 328, 322, 28, 492, 853, 332, 533, 933, 101, 290, 364, 47, 760, 257, 325, 656, 475, 811, 838, 616, 121, 694, 774, 120, 8, 47, 198, 284, 154, 477, 427, 915, 469, 137, 950, 208, 938, 787, 133, 759, 448, 911, 5, 594, 357, 677, 678, 987, 416, 608, 880, 743, 339, 342, 80, 726, 832, 48, 789, 911, 194, 100, 140, 923, 279, 618, 729, 405, 983, 940, 996, 241, 128, 937, 379, 771, 672, 716, 324, 511, 334, 868, 499, 80, 581, 404, 282, 695, 70, 448, 783, 518, 703, 238, 364, 307, 888, 876, 944, 307, 362, 17, 803, 89, 12, 763, 882, 91, 965, 594, 728, 815, 968, 570] The set of cells that are occupied is {3, 5, 7, 8, 12, 13, 17, 20, 25, 28, 29, 30, 34, 35, 38, 39, 40, 42, 46, 47, 48, 49, 50, 51, 52, 56, 57, 58, 63, 65, 69, 70, 71, 72, 73, 76, 78, 79, 80, 81, 83, 86, 89, 90, 91, 94, 95, 97, 98, 100, 101, 102, 103, 105, 106, 107, 108, 110, 112, 114, 118, 119, 120, 121, 123, 124, 125, 128, 129, 133, 134, 137, 138, 140, 142, 145, 146, 147, 148, 152, 154, 155, 156, 163, 166, 167, 168, 169, 170, 173, 177, 179, 181, 185, 188, 189, 191, 193, 194, 197, 198, 201, 202, 203, 206, 208, 209, 210, 211, 212, 213, 214, 217, 220, 223, 225, 228, 232, 236, 237, 238, 239, 241, 243, 248, 249, 252, 253, 257, 258, 261, 262, 263, 264, 274, 275, 279, 280, 282, 283, 284, 285, 286, 288, 290, 291, 292, 293, 299, 303, 306, 307, 308, 309, 311, 315, 317, 322, 324, 325, 326, 327, 328, 329, 332, 334, 339, 340, 342, 343, 345, 346, 349, 353, 354, 355, 356, 357, 360, 362, 364, 365, 367, 370, 372, 373, 374, 376, 378, 379, 382, 385, 387, 391, 394, 396, 398, 404, 405, 408, 409, 411, 413, 414, 415, 416, 418, 423, 427, 431, 433, 436, 444, 445, 448, 449, 452, 453, 456, 458, 459, 460, 461, 463, 466, 468, 469, 472, 474, 475, 477, 479, 481, 482, 483, 487, 488, 490, 491, 492, 497, 498, 499, 502, 503, 504, 506, 509, 511, 517, 518, 521, 528, 529, 530, 531, 532, 533, 535, 538, 539, 540, 542, 543, 546, 548, 550, 551, 552, 553, 560, 562, 564, 569, 570, 576, 577, 580, 581, 582, 588, 593, 594, 595, 597, 598, 599, 601, 602, 603, 604, 605, 607, 608, 609, 610, 611, 616, 617, 618, 622, 627, 630, 631, 632, 637, 639, 640, 641, 642, 644, 645, 646, 648, 651, 655, 656, 660, 662, 664, 666, 669, 671, 672, 673, 675, 677, 678, 680, 681, 683, 686, 688, 691, 694, 695, 701, 703, 706, 716, 721, 723, 726, 727, 728, 729, 730, 731, 734, 735, 738, 739, 741, 742, 743, 744, 746, 750, 754, 755, 756, 757, 759, 760, 761, 763, 764, 766, 767, 771, 772, 774, 778, 780, 781, 782, 783, 785, 786, 787, 788, 789, 793, 796, 797, 803, 805, 806, 807, 809, 811, 812, 814, 815, 816, 819, 821, 825, 831, 832, 833, 838, 846, 847, 849, 852, 853, 854, 857, 860, 862, 865, 866, 868, 869, 870, 872, 875, 876, 879, 880, 881, 882, 885, 886, 888, 889, 893, 895, 898, 899, 901, 902, 904, 907, 911, 912, 914, 915, 916, 917, 918, 920, 922, 923, 925, 930, 931, 933, 936, 937, 938, 940, 943, 944, 946, 947, 950, 952, 953, 954, 956, 959, 960, 962, 965, 968, 970, 971, 973, 977, 978, 982, 983, 985, 987, 996, 998, 1000} The set of cells that have exactly one ball in them is {3, 5, 7, 13, 20, 25, 28, 29, 30, 34, 35, 38, 39, 40, 46, 48, 49, 50, 52, 63, 65, 69, 71, 72, 73, 76, 79, 81, 83, 86, 89, 94, 97, 101, 102, 103, 105, 106, 107, 108, 110, 112, 114, 118, 119, 120, 123, 124, 125, 128, 129, 134, 137, 140, 142, 146, 147, 148, 152, 154, 155, 163, 166, 168, 169, 177, 179, 181, 185, 191, 193, 194, 201, 203, 206, 208, 209, 210, 212, 213, 214, 217, 223, 225, 228, 236, 237, 238, 239, 241, 243, 248, 252, 253, 258, 261, 262, 263, 264, 274, 275, 279, 280, 283, 284, 285, 286, 288, 291, 292, 293, 299, 303, 306, 308, 309, 311, 315, 317, 324, 325, 327, 340, 343, 346, 349, 353, 354, 355, 356, 360, 362, 365, 367, 372, 378, 379, 385, 387, 394, 396, 398, 405, 408, 409, 411, 413, 414, 415, 418, 423, 431, 433, 436, 444, 449, 452, 453, 456, 458, 459, 461, 463, 466, 472, 475, 477, 479, 482, 483, 487, 488, 490, 492, 497, 498, 499, 502, 503, 504, 506, 509, 517, 518, 521, 530, 531, 532, 538, 539, 540, 543, 546, 548, 550, 551, 552, 560, 562, 564, 570, 576, 577, 580, 581, 582, 588, 593, 595, 597, 598, 599, 601, 602, 603, 605, 609, 610, 611, 616, 617, 618, 622, 627, 630, 631, 632, 639, 640, 641, 642, 644, 646, 651, 655, 660, 664, 666, 671, 672, 673, 675, 677, 678, 680, 681, 683, 686, 688, 695, 706, 716, 721, 723, 726, 727, 728, 730, 731, 734, 735, 738, 739, 742, 743, 746, 750, 754, 755, 756, 757, 759, 760, 764, 767, 781, 782, 785, 786, 787, 788, 789, 793, 796, 797, 805, 806, 807, 811, 814, 816, 819, 821, 825, 831, 832, 833, 838, 846, 847, 849, 854, 857, 862, 865, 866, 868, 869, 870, 872, 875, 876, 879, 880, 881, 882, 885, 886, 888, 889, 893, 895, 898, 899, 901, 902, 904, 907, 914, 915, 916, 917, 920, 922, 923, 925, 930, 931, 933, 936, 937, 938, 940, 944, 946, 947, 950, 952, 954, 956, 959, 960, 965, 968, 973, 978, 982, 983, 985, 987, 996, 998} We remove these balls and are now left with, 267, balls The, 267, balls landed in the following cells [459, 937, 586, 652, 140, 776, 465, 346, 848, 442, 554, 850, 34, 17, 972, 875, 986, 534, 543, 920, 322, 450, 267, 705, 543, 807, 738, 984, 495, 655, 872, 242, 698, 81, 139, 958, 850, 267, 231, 82, 505, 76, 723, 547, 454, 908, 628, 783, 251, 166, 871, 385, 820, 750, 88, 450, 966, 457, 547, 7, 760, 207, 610, 224, 267, 999, 758, 919, 839, 135, 614, 863, 365, 259, 336, 214, 317, 296, 568, 296, 889, 964, 776, 175, 962, 250, 22, 286, 732, 490, 689, 742, 342, 763, 662, 565, 761, 985, 329, 950, 976, 669, 973, 489, 550, 927, 87, 518, 752, 136, 707, 283, 404, 352, 562, 586, 374, 746, 848, 269, 287, 685, 647, 35, 12, 683, 743, 633, 241, 234, 468, 351, 956, 197, 316, 945, 941, 523, 956, 608, 118, 509, 124, 994, 643, 237, 677, 342, 276, 551, 718, 627, 306, 510, 933, 809, 405, 27, 779, 294, 866, 59, 832, 618, 285, 389, 89, 508, 771, 355, 723, 662, 243, 509, 817, 447, 346, 151, 501, 573, 695, 431, 208, 736, 414, 879, 558, 680, 117, 945, 652, 532, 141, 550, 538, 555, 870, 282, 390, 577, 286, 645, 105, 934, 394, 762, 777, 622, 198, 18, 855, 907, 510, 861, 704, 821, 420, 460, 256, 252, 581, 377, 549, 521, 537, 948, 199, 254, 878, 197, 533, 954, 364, 550, 995, 611, 705, 21, 493, 808, 799, 786, 106, 553, 684, 690, 863, 375, 174, 720, 751, 383, 969, 439, 174, 442, 898, 917, 326, 967, 490, 673, 773, 151, 759, 714, 33] The set of cells that are occupied is {7, 12, 17, 18, 21, 22, 27, 33, 34, 35, 59, 76, 81, 82, 87, 88, 89, 105, 106, 117, 118, 124, 135, 136, 139, 140, 141, 151, 166, 174, 175, 197, 198, 199, 207, 208, 214, 224, 231, 234, 237, 241, 242, 243, 250, 251, 252, 254, 256, 259, 267, 269, 276, 282, 283, 285, 286, 287, 294, 296, 306, 316, 317, 322, 326, 329, 336, 342, 346, 351, 352, 355, 364, 365, 374, 375, 377, 383, 385, 389, 390, 394, 404, 405, 414, 420, 431, 439, 442, 447, 450, 454, 457, 459, 460, 465, 468, 489, 490, 493, 495, 501, 505, 508, 509, 510, 518, 521, 523, 532, 533, 534, 537, 538, 543, 547, 549, 550, 551, 553, 554, 555, 558, 562, 565, 568, 573, 577, 581, 586, 608, 610, 611, 614, 618, 622, 627, 628, 633, 643, 645, 647, 652, 655, 662, 669, 673, 677, 680, 683, 684, 685, 689, 690, 695, 698, 704, 705, 707, 714, 718, 720, 723, 732, 736, 738, 742, 743, 746, 750, 751, 752, 758, 759, 760, 761, 762, 763, 771, 773, 776, 777, 779, 783, 786, 799, 807, 808, 809, 817, 820, 821, 832, 839, 848, 850, 855, 861, 863, 866, 870, 871, 872, 875, 878, 879, 889, 898, 907, 908, 917, 919, 920, 927, 933, 934, 937, 941, 945, 948, 950, 954, 956, 958, 962, 964, 966, 967, 969, 972, 973, 976, 984, 985, 986, 994, 995, 999} The set of cells that have exactly one ball in them is {7, 12, 17, 18, 21, 22, 27, 33, 34, 35, 59, 76, 81, 82, 87, 88, 89, 105, 106, 117, 118, 124, 135, 136, 139, 140, 141, 166, 175, 198, 199, 207, 208, 214, 224, 231, 234, 237, 241, 242, 243, 250, 251, 252, 254, 256, 259, 269, 276, 282, 283, 285, 287, 294, 306, 316, 317, 322, 326, 329, 336, 351, 352, 355, 364, 365, 374, 375, 377, 383, 385, 389, 390, 394, 404, 405, 414, 420, 431, 439, 447, 454, 457, 459, 460, 465, 468, 489, 493, 495, 501, 505, 508, 518, 521, 523, 532, 533, 534, 537, 538, 549, 551, 553, 554, 555, 558, 562, 565, 568, 573, 577, 581, 608, 610, 611, 614, 618, 622, 627, 628, 633, 643, 645, 647, 655, 669, 673, 677, 680, 683, 684, 685, 689, 690, 695, 698, 704, 707, 714, 718, 720, 732, 736, 738, 742, 743, 746, 750, 751, 752, 758, 759, 760, 761, 762, 763, 771, 773, 777, 779, 783, 786, 799, 807, 808, 809, 817, 820, 821, 832, 839, 855, 861, 866, 870, 871, 872, 875, 878, 879, 889, 898, 907, 908, 917, 919, 920, 927, 933, 934, 937, 941, 948, 950, 954, 958, 962, 964, 966, 967, 969, 972, 973, 976, 984, 985, 986, 994, 995, 999} We remove these balls and are now left with, 56, balls The, 56, balls landed in the following cells [417, 294, 875, 706, 547, 55, 426, 252, 8, 647, 75, 70, 969, 708, 452, 668, 118, 716, 768, 792, 751, 103, 534, 463, 175, 907, 727, 597, 88, 534, 967, 541, 469, 5, 892, 492, 361, 821, 602, 577, 859, 249, 839, 197, 136, 389, 489, 243, 292, 544, 128, 406, 313, 930, 291, 210] The set of cells that are occupied is {5, 8, 55, 70, 75, 88, 103, 118, 128, 136, 175, 197, 210, 243, 249, 252, 291, 292, 294, 313, 361, 389, 406, 417, 426, 452, 463, 469, 489, 492, 534, 541, 544, 547, 577, 597, 602, 647, 668, 706, 708, 716, 727, 751, 768, 792, 821, 839, 859, 875, 892, 907, 930, 967, 969} The set of cells that have exactly one ball in them is {5, 8, 55, 70, 75, 88, 103, 118, 128, 136, 175, 197, 210, 243, 249, 252, 291, 292, 294, 313, 361, 389, 406, 417, 426, 452, 463, 469, 489, 492, 541, 544, 547, 577, 597, 602, 647, 668, 706, 708, 716, 727, 751, 768, 792, 821, 839, 859, 875, 892, 907, 930, 967, 969} We remove these balls and are now left with, 2, balls The, 2, balls landed in the following cells [425, 298] The set of cells that are occupied is {298, 425} The set of cells that have exactly one ball in them is {298, 425} We remove these balls and are now left with, 0, balls This took, 5, rounds --------------------------------------------------- This took, 0.232, seconds.