The trends in the Statistical Distribution of the Duration of the Dym-Luks B\ all and Cell Game with r balls and , r, cells as r grows larger By Shalosh B. Ekhad Suppose that you have r balls and (uniformly at) randomly throw them into , r . cells. Whenever a ball has no cell-mates, it is removed from the game\ and this continues until all the balls are removed We will give the average, standard deviation and moments up to the , 4, of the duration of the game for r from 2 to, 40 If there are , 2, balls and , 2, cells then The expectation, s.d, followed by the scaled moments up to the, 4, -th are [2., 1.414213562, 2.121320343, 9.500000000] --------------------------------------------- If there are , 3, balls and , 3, cells then The expectation, s.d, followed by the scaled moments up to the, 4, -th are [2.250000000, 1.060660172, 1.355287997, 6.388888889] --------------------------------------------- If there are , 4, balls and , 4, cells then The expectation, s.d, followed by the scaled moments up to the, 4, -th are [2.488888889, 0.9723756492, 1.182845567, 5.574179379] --------------------------------------------- If there are , 5, balls and , 5, cells then The expectation, s.d, followed by the scaled moments up to the, 4, -th are [2.665321265, 0.9155075842, 1.047031873, 4.875654509] --------------------------------------------- If there are , 6, balls and , 6, cells then The expectation, s.d, followed by the scaled moments up to the, 4, -th are [2.799230040, 0.8828373720, 0.9395293351, 4.408193786] --------------------------------------------- If there are , 7, balls and , 7, cells then The expectation, s.d, followed by the scaled moments up to the, 4, -th are [2.906491523, 0.8607667392, 0.8323841824, 4.078601823] --------------------------------------------- If there are , 8, balls and , 8, cells then The expectation, s.d, followed by the scaled moments up to the, 4, -th are [2.996492250, 0.8425947855, 0.7373864013, 3.881651407] --------------------------------------------- If there are , 9, balls and , 9, cells then The expectation, s.d, followed by the scaled moments up to the, 4, -th are [3.074151245, 0.8257361182, 0.6608740404, 3.776274907] --------------------------------------------- If there are , 10, balls and , 10, cells then The expectation, s.d, followed by the scaled moments up to the, 4, -th are [3.142213356, 0.8095280659, 0.6035761746, 3.725283571] --------------------------------------------- If there are , 11, balls and , 11, cells then The expectation, s.d, followed by the scaled moments up to the, 4, -th are [3.202458711, 0.7939827121, 0.5632516803, 3.701651626] --------------------------------------------- If there are , 12, balls and , 12, cells then The expectation, s.d, followed by the scaled moments up to the, 4, -th are [3.256189733, 0.7792790243, 0.5365823365, 3.687684677] --------------------------------------------- If there are , 13, balls and , 13, cells then The expectation, s.d, followed by the scaled moments up to the, 4, -th are [3.304425644, 0.7655819702, 0.5201244251, 3.672716471] --------------------------------------------- If there are , 14, balls and , 14, cells then The expectation, s.d, followed by the scaled moments up to the, 4, -th are [3.347993465, 0.7529893624, 0.5107363298, 3.651105812] --------------------------------------------- If there are , 15, balls and , 15, cells then The expectation, s.d, followed by the scaled moments up to the, 4, -th are [3.387577042, 0.7415286704, 0.5057532806, 3.620677582] --------------------------------------------- If there are , 16, balls and , 16, cells then The expectation, s.d, followed by the scaled moments up to the, 4, -th are [3.423746849, 0.7311711279, 0.5030392244, 3.581524821] --------------------------------------------- If there are , 17, balls and , 17, cells then The expectation, s.d, followed by the scaled moments up to the, 4, -th are [3.456980619, 0.7218490966, 0.5009737666, 3.535098340] --------------------------------------------- If there are , 18, balls and , 18, cells then The expectation, s.d, followed by the scaled moments up to the, 4, -th are [3.487679156, 0.7134714318, 0.4984030556, 3.483534136] --------------------------------------------- If there are , 19, balls and , 19, cells then The expectation, s.d, followed by the scaled moments up to the, 4, -th are [3.516179106, 0.7059354420, 0.4945718338, 3.429180345] --------------------------------------------- If there are , 20, balls and , 20, cells then The expectation, s.d, followed by the scaled moments up to the, 4, -th are [3.542763529, 0.6991355217, 0.4890484639, 3.374288319] --------------------------------------------- If there are , 21, balls and , 21, cells then The expectation, s.d, followed by the scaled moments up to the, 4, -th are [3.567670711, 0.6929689996, 0.4816512744, 3.320832728] --------------------------------------------- If there are , 22, balls and , 22, cells then The expectation, s.d, followed by the scaled moments up to the, 4, -th are [3.591101543, 0.6873398250, 0.4723817157, 3.270427038] --------------------------------------------- If there are , 23, balls and , 23, cells then The expectation, s.d, followed by the scaled moments up to the, 4, -th are [3.613225691, 0.6821606591, 0.4613673402, 3.224304376] --------------------------------------------- If there are , 24, balls and , 24, cells then The expectation, s.d, followed by the scaled moments up to the, 4, -th are [3.634186751, 0.6773538295, 0.4488156616, 3.183339154] --------------------------------------------- If there are , 25, balls and , 25, cells then The expectation, s.d, followed by the scaled moments up to the, 4, -th are [3.654106559, 0.6728515105, 0.4349785683, 3.148090758] --------------------------------------------- If there are , 26, balls and , 26, cells then The expectation, s.d, followed by the scaled moments up to the, 4, -th are [3.673088774, 0.6685953955, 0.4201261340, 3.118856205] --------------------------------------------- If there are , 27, balls and , 27, cells then The expectation, s.d, followed by the scaled moments up to the, 4, -th are [3.691221880, 0.6645360663, 0.4045282905, 3.095723344] --------------------------------------------- If there are , 28, balls and , 28, cells then The expectation, s.d, followed by the scaled moments up to the, 4, -th are [3.708581669, 0.6606321908, 0.3884427431, 3.078619766] --------------------------------------------- If there are , 29, balls and , 29, cells then The expectation, s.d, followed by the scaled moments up to the, 4, -th are [3.725233327, 0.6568496545, 0.3721076379, 3.067355076] --------------------------------------------- If there are , 30, balls and , 30, cells then The expectation, s.d, followed by the scaled moments up to the, 4, -th are [3.741233150, 0.6531606834, 0.3557376931, 3.061655833] --------------------------------------------- If there are , 31, balls and , 31, cells then The expectation, s.d, followed by the scaled moments up to the, 4, -th are [3.756629992, 0.6495430028, 0.3395227543, 3.061193421] --------------------------------------------- If there are , 32, balls and , 32, cells then The expectation, s.d, followed by the scaled moments up to the, 4, -th are [3.771466452, 0.6459790542, 0.3236279638, 3.065605618] --------------------------------------------- If there are , 33, balls and , 33, cells then The expectation, s.d, followed by the scaled moments up to the, 4, -th are [3.785779876, 0.6424552857, 0.3081949449, 3.074512826] --------------------------------------------- If there are , 34, balls and , 34, cells then The expectation, s.d, followed by the scaled moments up to the, 4, -th are [3.799603182, 0.6389615157, 0.2933435618, 3.087529954] --------------------------------------------- If there are , 35, balls and , 35, cells then The expectation, s.d, followed by the scaled moments up to the, 4, -th are [3.812965551, 0.6354903723, 0.2791739545, 3.104274861] --------------------------------------------- If there are , 36, balls and , 36, cells then The expectation, s.d, followed by the scaled moments up to the, 4, -th are [3.825893001, 0.6320368075, 0.2657686487, 3.124374139] --------------------------------------------- If there are , 37, balls and , 37, cells then The expectation, s.d, followed by the scaled moments up to the, 4, -th are [3.838408866, 0.6285976742, 0.2531946080, 3.147466898] --------------------------------------------- If there are , 38, balls and , 38, cells then The expectation, s.d, followed by the scaled moments up to the, 4, -th are [3.850534195, 0.6251713649, 0.2415051554, 3.173207077] --------------------------------------------- If there are , 39, balls and , 39, cells then The expectation, s.d, followed by the scaled moments up to the, 4, -th are [3.862288083, 0.6217575055, 0.2307417247, 3.201264681] --------------------------------------------- If there are , 40, balls and , 40, cells then The expectation, s.d, followed by the scaled moments up to the, 4, -th are [3.873687955, 0.6183566945, 0.2209354208, 3.231326280] --------------------------------------------- ----------------------------- This ends this paper that took, 214.856, to produce.