For the problem of deciding in, 2, weighings of a balance scale, which of , 3, coins is fake, and whether it is heavier and lighter, give them the following code names (row i is a code nam\ e for code i) [ 1 0] [ ] [-1 1] [ ] [ 0 -1] This implies that In weighing number, 1, place the coins in , {1}, on the left side and the coins in, {2}, on the right side In weighing number, 2, place the coins in , {2}, on the left side and the coins in, {3}, on the right side ----------------------------- For the problem of deciding in, 3, weighings of a balance scale, which of , 12, coins is fake, and whether it is heavier and lighter, give them the following code names (row i is a code nam\ e for code i) [ 1 1 0] [ ] [-1 -1 1] [ ] [-1 0 -1] [ ] [ 1 0 0] [ ] [ 1 0 -1] [ ] [-1 1 -1] [ ] [-1 1 0] [ ] [ 1 -1 -1] [ ] [ 0 1 1] [ ] [ 0 -1 0] [ ] [ 0 -1 1] [ ] [ 0 0 1] This implies that In weighing number, 1, place the coins in , {1, 4, 5, 8}, on the left side and the coins in, {2, 3, 6, 7}, on the right side In weighing number, 2, place the coins in , {1, 6, 7, 9}, on the left side and the coins in, {2, 8, 10, 11}, on the right side In weighing number, 3, place the coins in , {2, 9, 11, 12}, on the left side and the coins in, {3, 5, 6, 8}, on the right side ----------------------------- For the problem of deciding in, 4, weighings of a balance scale, which of , 39, coins is fake, and whether it is heavier and lighter, give them the following code names (row i is a code nam\ e for code i) [-1 -1 -1 0] [ ] [ 1 1 1 -1] [ ] [-1 -1 0 -1] [ ] [ 1 1 0 0] [ ] [-1 -1 0 1] [ ] [ 1 1 -1 1] [ ] [ 1 1 -1 0] [ ] [ 1 1 -1 -1] [ ] [ 1 0 1 1] [ ] [-1 0 -1 0] [ ] [-1 0 -1 1] [ ] [-1 0 0 -1] [ ] [ 1 0 0 0] [ ] [-1 0 0 1] [ ] [-1 0 1 -1] [ ] [-1 0 1 0] [ ] [ 1 0 -1 -1] [ ] [ 1 -1 1 1] [ ] [-1 1 -1 0] [ ] [-1 1 -1 1] [ ] [ 1 -1 0 1] [ ] [ 1 -1 0 0] [ ] [ 1 -1 0 -1] [ ] [ 1 -1 -1 1] [ ] [-1 1 1 0] [ ] [-1 1 1 1] [ ] [ 0 -1 -1 -1] [ ] [ 0 1 1 0] [ ] [ 0 -1 -1 1] [ ] [ 0 1 0 1] [ ] [ 0 1 0 0] [ ] [ 0 1 0 -1] [ ] [ 0 -1 1 -1] [ ] [ 0 -1 1 0] [ ] [ 0 -1 1 1] [ ] [ 0 0 -1 -1] [ ] [ 0 0 1 0] [ ] [ 0 0 1 -1] [ ] [ 0 0 0 -1] This implies that In weighing number, 1, place the coins in , {2, 4, 6, 7, 8, 9, 13, 17, 18, 21, 22, 23, 24}, on the left side and the coins in, {1, 3, 5, 10, 11, 12, 14, 15, 16, 19, 20, 25, 26}, on the right side In weighing number, 2, place the coins in , {2, 4, 6, 7, 8, 19, 20, 25, 26, 28, 30, 31, 32}, on the left side and the coins in, {1, 3, 5, 18, 21, 22, 23, 24, 27, 29, 33, 34, 35}, on the right side In weighing number, 3, place the coins in , {2, 9, 15, 16, 18, 25, 26, 28, 33, 34, 35, 37, 38}, on the left side and the coins in, {1, 6, 7, 8, 10, 11, 17, 19, 20, 24, 27, 29, 36}, on the right side In weighing number, 4, place the coins in , {5, 6, 9, 11, 14, 18, 20, 21, 24, 26, 29, 30, 35}, on the left side and the coins in, {2, 3, 8, 12, 15, 17, 23, 27, 32, 33, 36, 38, 39}, on the right side ----------------------------- For the problem of deciding in, 5, weighings of a balance scale, which of , 120, coins is fake, and whether it is heavier and lighter, give them the following code names (row i is a code nam\ e for code i) [-1 -1 -1 -1 0] [ ] [-1 -1 -1 -1 1] [ ] [ 1 1 1 0 1] [ ] [ 1 1 1 0 0] [ ] [-1 -1 -1 0 1] [ ] [ 1 1 1 -1 1] [ ] [ 1 1 1 -1 0] [ ] [ 1 1 1 -1 -1] [ ] [-1 -1 0 -1 -1] [ ] [-1 -1 0 -1 0] [ ] [-1 -1 0 -1 1] [ ] [-1 -1 0 0 -1] [ ] [-1 -1 0 0 0] [ ] [-1 -1 0 0 1] [ ] [ 1 1 0 -1 1] [ ] [ 1 1 0 -1 0] [ ] [ 1 1 0 -1 -1] [ ] [-1 -1 1 -1 -1] [ ] [ 1 1 -1 1 0] [ ] [ 1 1 -1 1 -1] [ ] [ 1 1 -1 0 1] [ ] [-1 -1 1 0 0] [ ] [ 1 1 -1 0 -1] [ ] [-1 -1 1 1 -1] [ ] [-1 -1 1 1 0] [ ] [-1 -1 1 1 1] [ ] [ 1 0 1 1 1] [ ] [ 1 0 1 1 0] [ ] [ 1 0 1 1 -1] [ ] [ 1 0 1 0 1] [ ] [-1 0 -1 0 0] [ ] [ 1 0 1 0 -1] [ ] [-1 0 -1 1 -1] [ ] [ 1 0 1 -1 0] [ ] [-1 0 -1 1 1] [ ] [ 1 0 0 1 1] [ ] [ 1 0 0 1 0] [ ] [-1 0 0 -1 1] [ ] [-1 0 0 0 -1] [ ] [ 1 0 0 0 0] [ ] [ 1 0 0 0 -1] [ ] [-1 0 0 1 -1] [ ] [-1 0 0 1 0] [ ] [ 1 0 0 -1 -1] [ ] [-1 0 1 -1 -1] [ ] [-1 0 1 -1 0] [ ] [ 1 0 -1 1 -1] [ ] [ 1 0 -1 0 1] [ ] [-1 0 1 0 0] [ ] [-1 0 1 0 1] [ ] [-1 0 1 1 -1] [ ] [-1 0 1 1 0] [ ] [ 1 0 -1 -1 -1] [ ] [-1 1 -1 -1 -1] [ ] [ 1 -1 1 1 0] [ ] [ 1 -1 1 1 -1] [ ] [ 1 -1 1 0 1] [ ] [-1 1 -1 0 0] [ ] [ 1 -1 1 0 -1] [ ] [-1 1 -1 1 -1] [ ] [-1 1 -1 1 0] [ ] [-1 1 -1 1 1] [ ] [-1 1 0 -1 -1] [ ] [ 1 -1 0 1 0] [ ] [-1 1 0 -1 1] [ ] [-1 1 0 0 -1] [ ] [ 1 -1 0 0 0] [ ] [-1 1 0 0 1] [ ] [ 1 -1 0 -1 1] [ ] [ 1 -1 0 -1 0] [ ] [ 1 -1 0 -1 -1] [ ] [ 1 -1 -1 1 1] [ ] [ 1 -1 -1 1 0] [ ] [ 1 -1 -1 1 -1] [ ] [-1 1 1 0 -1] [ ] [ 1 -1 -1 0 0] [ ] [ 1 -1 -1 0 -1] [ ] [-1 1 1 1 -1] [ ] [-1 1 1 1 0] [ ] [-1 1 1 1 1] [ ] [ 0 -1 -1 -1 -1] [ ] [ 0 1 1 1 0] [ ] [ 0 -1 -1 -1 1] [ ] [ 0 -1 -1 0 -1] [ ] [ 0 -1 -1 0 0] [ ] [ 0 1 1 0 -1] [ ] [ 0 -1 -1 1 -1] [ ] [ 0 -1 -1 1 0] [ ] [ 0 -1 -1 1 1] [ ] [ 0 -1 0 -1 -1] [ ] [ 0 1 0 1 0] [ ] [ 0 -1 0 -1 1] [ ] [ 0 1 0 0 1] [ ] [ 0 1 0 0 0] [ ] [ 0 1 0 0 -1] [ ] [ 0 1 0 -1 1] [ ] [ 0 1 0 -1 0] [ ] [ 0 -1 0 1 1] [ ] [ 0 1 -1 1 1] [ ] [ 0 -1 1 -1 0] [ ] [ 0 -1 1 -1 1] [ ] [ 0 1 -1 0 1] [ ] [ 0 1 -1 0 0] [ ] [ 0 1 -1 0 -1] [ ] [ 0 1 -1 -1 1] [ ] [ 0 1 -1 -1 0] [ ] [ 0 1 -1 -1 -1] [ ] [ 0 0 1 1 1] [ ] [ 0 0 1 1 0] [ ] [ 0 0 -1 -1 1] [ ] [ 0 0 1 0 1] [ ] [ 0 0 -1 0 0] [ ] [ 0 0 1 0 -1] [ ] [ 0 0 1 -1 1] [ ] [ 0 0 1 -1 0] [ ] [ 0 0 -1 1 1] [ ] [ 0 0 0 1 1] [ ] [ 0 0 0 -1 0] [ ] [ 0 0 0 -1 1] [ ] [ 0 0 0 0 -1] This implies that In weighing number, 1, place the coins in , {3, 4, 6, 7, 8, 15, 16, 17, 19, 20, 21, 23, 27, 28, 29, 30, 32, 34, 36, 37, 40, 41, 44, 47, 48, 53, 55, 56, 57, 59, 64, 67, 69, 70, 71, 72, 73, 74, 76, 77}, on the left side and the coins in, {1, 2, 5, 9, 10, 11, 12, 13, 14, 18, 22, 24, 25, 26, 31, 33, 35, 38, 39, 42, 43, 45, 46, 49, 50, 51, 52, 54, 58, 60, 61, 62, 63, 65, 66, 68, 75, 78, 79, 80}, on the right side In weighing number, 2, place the coins in , {3, 4, 6, 7, 8, 15, 16, 17, 19, 20, 21, 23, 54, 58, 60, 61, 62, 63, 65, 66, 68, 75, 78, 79, 80, 82, 86, 91, 93, 94, 95, 96, 97, 99, 102, 103, 104, 105, 106, 107}, on the left side and the coins in, {1, 2, 5, 9, 10, 11, 12, 13, 14, 18, 22, 24, 25, 26, 55, 56, 57, 59, 64, 67, 69, 70, 71, 72, 73, 74, 76, 77, 81, 83, 84, 85, 87, 88, 89, 90, 92, 98, 100, 101}, on the right side In weighing number, 3, place the coins in , {3, 4, 6, 7, 8, 18, 22, 24, 25, 26, 27, 28, 29, 30, 32, 34, 45, 46, 49, 50, 51, 52, 55, 56, 57, 59, 75, 78, 79, 80, 82, 86, 100, 101, 108, 109, 111, 113, 114, 115}, on the left side and the coins in, {1, 2, 5, 19, 20, 21, 23, 31, 33, 35, 47, 48, 53, 54, 58, 60, 61, 62, 72, 73, 74, 76, 77, 81, 83, 84, 85, 87, 88, 89, 99, 102, 103, 104, 105, 106, 107, 110, 112, 116}, on the right side In weighing number, 4, place the coins in , {19, 20, 24, 25, 26, 27, 28, 29, 33, 35, 36, 37, 42, 43, 47, 51, 52, 55, 56, 60, 61, 62, 64, 72, 73, 74, 78, 79, 80, 82, 87, 88, 89, 91, 98, 99, 108, 109, 116, 117}, on the left side and the coins in, {1, 2, 6, 7, 8, 9, 10, 11, 15, 16, 17, 18, 34, 38, 44, 45, 46, 53, 54, 63, 65, 69, 70, 71, 81, 83, 90, 92, 96, 97, 100, 101, 105, 106, 107, 110, 114, 115, 118, 119}, on the right side In weighing number, 5, place the coins in , {2, 3, 5, 6, 11, 14, 15, 21, 26, 27, 30, 35, 36, 38, 48, 50, 57, 62, 65, 68, 69, 72, 80, 83, 89, 92, 93, 96, 98, 99, 101, 102, 105, 108, 110, 111, 114, 116, 117, 119}, on the left side and the coins in, {8, 9, 12, 17, 18, 20, 23, 24, 29, 32, 33, 39, 41, 42, 44, 45, 47, 51, 53, 54, 56, 59, 60, 63, 66, 71, 74, 75, 77, 78, 81, 84, 86, 87, 90, 95, 104, 107, 113, 120}, on the right side ----------------------------- For the problem of deciding in, 6, weighings of a balance scale, which of , 363, coins is fake, and whether it is heavier and lighter, give them the following code names (row i is a code nam\ e for code i) [-1 -1 -1 -1 -1 0] [ ] [ 1 1 1 1 1 -1] [ ] [ 1 1 1 1 0 1] [ ] [-1 -1 -1 -1 0 0] [ ] [ 1 1 1 1 0 -1] [ ] [ 1 1 1 1 -1 1] [ ] [ 1 1 1 1 -1 0] [ ] [-1 -1 -1 -1 1 1] [ ] [-1 -1 -1 0 -1 -1] [ ] [-1 -1 -1 0 -1 0] [ ] [ 1 1 1 0 1 -1] [ ] [-1 -1 -1 0 0 -1] [ ] [-1 -1 -1 0 0 0] [ ] [-1 -1 -1 0 0 1] [ ] [-1 -1 -1 0 1 -1] [ ] [ 1 1 1 0 -1 0] [ ] [ 1 1 1 0 -1 -1] [ ] [-1 -1 -1 1 -1 -1] [ ] [-1 -1 -1 1 -1 0] [ ] [ 1 1 1 -1 1 -1] [ ] [-1 -1 -1 1 0 -1] [ ] [-1 -1 -1 1 0 0] [ ] [ 1 1 1 -1 0 -1] [ ] [ 1 1 1 -1 -1 1] [ ] [ 1 1 1 -1 -1 0] [ ] [ 1 1 1 -1 -1 -1] [ ] [ 1 1 0 1 1 1] [ ] [-1 -1 0 -1 -1 0] [ ] [ 1 1 0 1 1 -1] [ ] [-1 -1 0 -1 0 -1] [ ] [ 1 1 0 1 0 0] [ ] [-1 -1 0 -1 0 1] [ ] [ 1 1 0 1 -1 1] [ ] [-1 -1 0 -1 1 0] [ ] [ 1 1 0 1 -1 -1] [ ] [ 1 1 0 0 1 1] [ ] [-1 -1 0 0 -1 0] [ ] [-1 -1 0 0 -1 1] [ ] [-1 -1 0 0 0 -1] [ ] [ 1 1 0 0 0 0] [ ] [-1 -1 0 0 0 1] [ ] [-1 -1 0 0 1 -1] [ ] [-1 -1 0 0 1 0] [ ] [-1 -1 0 0 1 1] [ ] [ 1 1 0 -1 1 1] [ ] [-1 -1 0 1 -1 0] [ ] [ 1 1 0 -1 1 -1] [ ] [ 1 1 0 -1 0 1] [ ] [ 1 1 0 -1 0 0] [ ] [ 1 1 0 -1 0 -1] [ ] [ 1 1 0 -1 -1 1] [ ] [-1 -1 0 1 1 0] [ ] [-1 -1 0 1 1 1] [ ] [-1 -1 1 -1 -1 -1] [ ] [ 1 1 -1 1 1 0] [ ] [ 1 1 -1 1 1 -1] [ ] [-1 -1 1 -1 0 -1] [ ] [ 1 1 -1 1 0 0] [ ] [ 1 1 -1 1 0 -1] [ ] [-1 -1 1 -1 1 -1] [ ] [ 1 1 -1 1 -1 0] [ ] [ 1 1 -1 1 -1 -1] [ ] [ 1 1 -1 0 1 1] [ ] [-1 -1 1 0 -1 0] [ ] [ 1 1 -1 0 1 -1] [ ] [-1 -1 1 0 0 -1] [ ] [ 1 1 -1 0 0 0] [ ] [-1 -1 1 0 0 1] [ ] [-1 -1 1 0 1 -1] [ ] [-1 -1 1 0 1 0] [ ] [-1 -1 1 0 1 1] [ ] [-1 -1 1 1 -1 -1] [ ] [ 1 1 -1 -1 1 0] [ ] [-1 -1 1 1 -1 1] [ ] [-1 -1 1 1 0 -1] [ ] [ 1 1 -1 -1 0 0] [ ] [ 1 1 -1 -1 0 -1] [ ] [ 1 1 -1 -1 -1 1] [ ] [-1 -1 1 1 1 0] [ ] [-1 -1 1 1 1 1] [ ] [ 1 0 1 1 1 1] [ ] [-1 0 -1 -1 -1 0] [ ] [ 1 0 1 1 1 -1] [ ] [-1 0 -1 -1 0 -1] [ ] [-1 0 -1 -1 0 0] [ ] [ 1 0 1 1 0 -1] [ ] [-1 0 -1 -1 1 -1] [ ] [ 1 0 1 1 -1 0] [ ] [-1 0 -1 -1 1 1] [ ] [-1 0 -1 0 -1 -1] [ ] [-1 0 -1 0 -1 0] [ ] [-1 0 -1 0 -1 1] [ ] [ 1 0 1 0 0 1] [ ] [ 1 0 1 0 0 0] [ ] [-1 0 -1 0 0 1] [ ] [ 1 0 1 0 -1 1] [ ] [ 1 0 1 0 -1 0] [ ] [-1 0 -1 0 1 1] [ ] [ 1 0 1 -1 1 1] [ ] [-1 0 -1 1 -1 0] [ ] [ 1 0 1 -1 1 -1] [ ] [ 1 0 1 -1 0 1] [ ] [-1 0 -1 1 0 0] [ ] [-1 0 -1 1 0 1] [ ] [-1 0 -1 1 1 -1] [ ] [-1 0 -1 1 1 0] [ ] [-1 0 -1 1 1 1] [ ] [-1 0 0 -1 -1 -1] [ ] [ 1 0 0 1 1 0] [ ] [-1 0 0 -1 -1 1] [ ] [ 1 0 0 1 0 1] [ ] [-1 0 0 -1 0 0] [ ] [ 1 0 0 1 0 -1] [ ] [-1 0 0 -1 1 -1] [ ] [ 1 0 0 1 -1 0] [ ] [-1 0 0 -1 1 1] [ ] [-1 0 0 0 -1 -1] [ ] [-1 0 0 0 -1 0] [ ] [ 1 0 0 0 1 -1] [ ] [-1 0 0 0 0 -1] [ ] [ 1 0 0 0 0 0] [ ] [-1 0 0 0 0 1] [ ] [ 1 0 0 0 -1 1] [ ] [-1 0 0 0 1 0] [ ] [ 1 0 0 0 -1 -1] [ ] [ 1 0 0 -1 1 1] [ ] [-1 0 0 1 -1 0] [ ] [-1 0 0 1 -1 1] [ ] [ 1 0 0 -1 0 1] [ ] [ 1 0 0 -1 0 0] [ ] [ 1 0 0 -1 0 -1] [ ] [ 1 0 0 -1 -1 1] [ ] [ 1 0 0 -1 -1 0] [ ] [ 1 0 0 -1 -1 -1] [ ] [ 1 0 -1 1 1 1] [ ] [ 1 0 -1 1 1 0] [ ] [ 1 0 -1 1 1 -1] [ ] [-1 0 1 -1 0 -1] [ ] [ 1 0 -1 1 0 0] [ ] [ 1 0 -1 1 0 -1] [ ] [ 1 0 -1 1 -1 1] [ ] [ 1 0 -1 1 -1 0] [ ] [-1 0 1 -1 1 1] [ ] [-1 0 1 0 -1 -1] [ ] [-1 0 1 0 -1 0] [ ] [-1 0 1 0 -1 1] [ ] [ 1 0 -1 0 0 1] [ ] [ 1 0 -1 0 0 0] [ ] [ 1 0 -1 0 0 -1] [ ] [ 1 0 -1 0 -1 1] [ ] [-1 0 1 0 1 0] [ ] [-1 0 1 0 1 1] [ ] [-1 0 1 1 -1 -1] [ ] [-1 0 1 1 -1 0] [ ] [ 1 0 -1 -1 1 -1] [ ] [-1 0 1 1 0 -1] [ ] [-1 0 1 1 0 0] [ ] [-1 0 1 1 0 1] [ ] [ 1 0 -1 -1 -1 1] [ ] [ 1 0 -1 -1 -1 0] [ ] [ 1 0 -1 -1 -1 -1] [ ] [ 1 -1 1 1 1 1] [ ] [-1 1 -1 -1 -1 0] [ ] [ 1 -1 1 1 1 -1] [ ] [-1 1 -1 -1 0 -1] [ ] [ 1 -1 1 1 0 0] [ ] [ 1 -1 1 1 0 -1] [ ] [-1 1 -1 -1 1 -1] [ ] [-1 1 -1 -1 1 0] [ ] [ 1 -1 1 1 -1 -1] [ ] [ 1 -1 1 0 1 1] [ ] [-1 1 -1 0 -1 0] [ ] [ 1 -1 1 0 1 -1] [ ] [-1 1 -1 0 0 -1] [ ] [-1 1 -1 0 0 0] [ ] [-1 1 -1 0 0 1] [ ] [-1 1 -1 0 1 -1] [ ] [ 1 -1 1 0 -1 0] [ ] [ 1 -1 1 0 -1 -1] [ ] [ 1 -1 1 -1 1 1] [ ] [ 1 -1 1 -1 1 0] [ ] [-1 1 -1 1 -1 1] [ ] [-1 1 -1 1 0 -1] [ ] [ 1 -1 1 -1 0 0] [ ] [ 1 -1 1 -1 0 -1] [ ] [-1 1 -1 1 1 -1] [ ] [ 1 -1 1 -1 -1 0] [ ] [ 1 -1 1 -1 -1 -1] [ ] [ 1 -1 0 1 1 1] [ ] [ 1 -1 0 1 1 0] [ ] [-1 1 0 -1 -1 1] [ ] [-1 1 0 -1 0 -1] [ ] [-1 1 0 -1 0 0] [ ] [-1 1 0 -1 0 1] [ ] [ 1 -1 0 1 -1 1] [ ] [-1 1 0 -1 1 0] [ ] [-1 1 0 -1 1 1] [ ] [ 1 -1 0 0 1 1] [ ] [ 1 -1 0 0 1 0] [ ] [ 1 -1 0 0 1 -1] [ ] [ 1 -1 0 0 0 1] [ ] [ 1 -1 0 0 0 0] [ ] [-1 1 0 0 0 1] [ ] [ 1 -1 0 0 -1 1] [ ] [-1 1 0 0 1 0] [ ] [ 1 -1 0 0 -1 -1] [ ] [ 1 -1 0 -1 1 1] [ ] [-1 1 0 1 -1 0] [ ] [-1 1 0 1 -1 1] [ ] [ 1 -1 0 -1 0 1] [ ] [ 1 -1 0 -1 0 0] [ ] [-1 1 0 1 0 1] [ ] [-1 1 0 1 1 -1] [ ] [-1 1 0 1 1 0] [ ] [-1 1 0 1 1 1] [ ] [ 1 -1 -1 1 1 1] [ ] [-1 1 1 -1 -1 0] [ ] [ 1 -1 -1 1 1 -1] [ ] [-1 1 1 -1 0 -1] [ ] [-1 1 1 -1 0 0] [ ] [ 1 -1 -1 1 0 -1] [ ] [-1 1 1 -1 1 -1] [ ] [-1 1 1 -1 1 0] [ ] [-1 1 1 -1 1 1] [ ] [ 1 -1 -1 0 1 1] [ ] [-1 1 1 0 -1 0] [ ] [-1 1 1 0 -1 1] [ ] [ 1 -1 -1 0 0 1] [ ] [ 1 -1 -1 0 0 0] [ ] [-1 1 1 0 0 1] [ ] [-1 1 1 0 1 -1] [ ] [-1 1 1 0 1 0] [ ] [-1 1 1 0 1 1] [ ] [ 1 -1 -1 -1 1 1] [ ] [ 1 -1 -1 -1 1 0] [ ] [ 1 -1 -1 -1 1 -1] [ ] [ 1 -1 -1 -1 0 1] [ ] [-1 1 1 1 0 0] [ ] [ 1 -1 -1 -1 0 -1] [ ] [ 1 -1 -1 -1 -1 1] [ ] [-1 1 1 1 1 0] [ ] [ 1 -1 -1 -1 -1 -1] [ ] [ 0 1 1 1 1 1] [ ] [ 0 1 1 1 1 0] [ ] [ 0 -1 -1 -1 -1 1] [ ] [ 0 1 1 1 0 1] [ ] [ 0 1 1 1 0 0] [ ] [ 0 -1 -1 -1 0 1] [ ] [ 0 1 1 1 -1 1] [ ] [ 0 1 1 1 -1 0] [ ] [ 0 -1 -1 -1 1 1] [ ] [ 0 1 1 0 1 1] [ ] [ 0 -1 -1 0 -1 0] [ ] [ 0 -1 -1 0 -1 1] [ ] [ 0 -1 -1 0 0 -1] [ ] [ 0 1 1 0 0 0] [ ] [ 0 -1 -1 0 0 1] [ ] [ 0 1 1 0 -1 1] [ ] [ 0 1 1 0 -1 0] [ ] [ 0 1 1 0 -1 -1] [ ] [ 0 1 1 -1 1 1] [ ] [ 0 -1 -1 1 -1 0] [ ] [ 0 1 1 -1 1 -1] [ ] [ 0 1 1 -1 0 1] [ ] [ 0 -1 -1 1 0 0] [ ] [ 0 -1 -1 1 0 1] [ ] [ 0 -1 -1 1 1 -1] [ ] [ 0 1 1 -1 -1 0] [ ] [ 0 1 1 -1 -1 -1] [ ] [ 0 -1 0 -1 -1 -1] [ ] [ 0 -1 0 -1 -1 0] [ ] [ 0 1 0 1 1 -1] [ ] [ 0 -1 0 -1 0 -1] [ ] [ 0 -1 0 -1 0 0] [ ] [ 0 -1 0 -1 0 1] [ ] [ 0 -1 0 -1 1 -1] [ ] [ 0 1 0 1 -1 0] [ ] [ 0 1 0 1 -1 -1] [ ] [ 0 1 0 0 1 1] [ ] [ 0 -1 0 0 -1 0] [ ] [ 0 -1 0 0 -1 1] [ ] [ 0 -1 0 0 0 -1] [ ] [ 0 -1 0 0 0 0] [ ] [ 0 1 0 0 0 -1] [ ] [ 0 1 0 0 -1 1] [ ] [ 0 -1 0 0 1 0] [ ] [ 0 1 0 0 -1 -1] [ ] [ 0 -1 0 1 -1 -1] [ ] [ 0 -1 0 1 -1 0] [ ] [ 0 1 0 -1 1 -1] [ ] [ 0 1 0 -1 0 1] [ ] [ 0 -1 0 1 0 0] [ ] [ 0 -1 0 1 0 1] [ ] [ 0 1 0 -1 -1 1] [ ] [ 0 -1 0 1 1 0] [ ] [ 0 -1 0 1 1 1] [ ] [ 0 1 -1 1 1 1] [ ] [ 0 -1 1 -1 -1 0] [ ] [ 0 1 -1 1 1 -1] [ ] [ 0 1 -1 1 0 1] [ ] [ 0 -1 1 -1 0 0] [ ] [ 0 1 -1 1 0 -1] [ ] [ 0 -1 1 -1 1 -1] [ ] [ 0 1 -1 1 -1 0] [ ] [ 0 -1 1 -1 1 1] [ ] [ 0 -1 1 0 -1 -1] [ ] [ 0 1 -1 0 1 0] [ ] [ 0 1 -1 0 1 -1] [ ] [ 0 1 -1 0 0 1] [ ] [ 0 1 -1 0 0 0] [ ] [ 0 1 -1 0 0 -1] [ ] [ 0 -1 1 0 1 -1] [ ] [ 0 1 -1 0 -1 0] [ ] [ 0 1 -1 0 -1 -1] [ ] [ 0 1 -1 -1 1 1] [ ] [ 0 -1 1 1 -1 0] [ ] [ 0 -1 1 1 -1 1] [ ] [ 0 -1 1 1 0 -1] [ ] [ 0 1 -1 -1 0 0] [ ] [ 0 -1 1 1 0 1] [ ] [ 0 -1 1 1 1 -1] [ ] [ 0 1 -1 -1 -1 0] [ ] [ 0 1 -1 -1 -1 -1] [ ] [ 0 0 -1 -1 -1 -1] [ ] [ 0 0 1 1 1 0] [ ] [ 0 0 1 1 1 -1] [ ] [ 0 0 -1 -1 0 -1] [ ] [ 0 0 1 1 0 0] [ ] [ 0 0 -1 -1 0 1] [ ] [ 0 0 1 1 -1 1] [ ] [ 0 0 1 1 -1 0] [ ] [ 0 0 1 1 -1 -1] [ ] [ 0 0 1 0 1 1] [ ] [ 0 0 -1 0 -1 0] [ ] [ 0 0 -1 0 -1 1] [ ] [ 0 0 -1 0 0 -1] [ ] [ 0 0 -1 0 0 0] [ ] [ 0 0 -1 0 0 1] [ ] [ 0 0 1 0 -1 1] [ ] [ 0 0 1 0 -1 0] [ ] [ 0 0 1 0 -1 -1] [ ] [ 0 0 -1 1 -1 -1] [ ] [ 0 0 1 -1 1 0] [ ] [ 0 0 1 -1 1 -1] [ ] [ 0 0 1 -1 0 1] [ ] [ 0 0 -1 1 0 0] [ ] [ 0 0 1 -1 0 -1] [ ] [ 0 0 -1 1 1 -1] [ ] [ 0 0 1 -1 -1 0] [ ] [ 0 0 -1 1 1 1] [ ] [ 0 0 0 1 1 1] [ ] [ 0 0 0 1 1 0] [ ] [ 0 0 0 -1 -1 1] [ ] [ 0 0 0 -1 0 -1] [ ] [ 0 0 0 1 0 0] [ ] [ 0 0 0 -1 0 1] [ ] [ 0 0 0 -1 1 -1] [ ] [ 0 0 0 1 -1 0] [ ] [ 0 0 0 -1 1 1] [ ] [ 0 0 0 0 -1 -1] [ ] [ 0 0 0 0 1 0] [ ] [ 0 0 0 0 1 -1] [ ] [ 0 0 0 0 0 1] This implies that In weighing number, 1, place the coins in , {2, 3, 5, 6, 7, 11, 16, 17, 20, 23, 24, 25, 26, 27, 29, 31, 33, 35, 36, 40, 45, 47, 48, 49, 50, 51, 55, 56, 58, 59, 61, 62, 63, 65, 67, 73, 76, 77, 78, 81, 83, 86, 88, 93, 94, 96, 97, 99, 101, 102, 109, 111, 113, 115, 119, 121, 123, 125, 126, 129, 130, 131, 132, 133, 134, 135, 136, 137, 139, 140, 141, 142, 147, 148, 149, 150, 155, 159, 160, 161, 162, 164, 166, 167, 170, 171, 173, 178, 179, 180, 181, 184, 185, 187, 188, 189, 190, 195, 198, 199, 200, 201, 202, 204, 206, 207, 210, 211, 216, 218, 221, 225, 228, 229, 234, 235, 236, 237, 239, 240, 242}, on the left side and the coins in, {1, 4, 8, 9, 10, 12, 13, 14, 15, 18, 19, 21, 22, 28, 30, 32, 34, 37, 38, 39, 41, 42, 43, 44, 46, 52, 53, 54, 57, 60, 64, 66, 68, 69, 70, 71, 72, 74, 75, 79, 80, 82, 84, 85, 87, 89, 90, 91, 92, 95, 98, 100, 103, 104, 105, 106, 107, 108, 110, 112, 114, 116, 117, 118, 120, 122, 124, 127, 128, 138, 143, 144, 145, 146, 151, 152, 153, 154, 156, 157, 158, 163, 165, 168, 169, 172, 174, 175, 176, 177, 182, 183, 186, 191, 192, 193, 194, 196, 197, 203, 205, 208, 209, 212, 213, 214, 215, 217, 219, 220, 222, 223, 224, 226, 227, 230, 231, 232, 233, 238, 241}, on the right side In weighing number, 2, place the coins in , {2, 3, 5, 6, 7, 11, 16, 17, 20, 23, 24, 25, 26, 27, 29, 31, 33, 35, 36, 40, 45, 47, 48, 49, 50, 51, 55, 56, 58, 59, 61, 62, 63, 65, 67, 73, 76, 77, 78, 163, 165, 168, 169, 172, 174, 175, 176, 177, 182, 183, 186, 191, 192, 193, 194, 196, 197, 203, 205, 208, 209, 212, 213, 214, 215, 217, 219, 220, 222, 223, 224, 226, 227, 230, 231, 232, 233, 238, 241, 243, 244, 246, 247, 249, 250, 252, 256, 258, 259, 260, 261, 263, 264, 268, 269, 272, 277, 278, 279, 284, 285, 287, 290, 291, 294, 297, 299, 300, 302, 304, 307, 308, 309, 310, 311, 313, 314, 315, 319, 322, 323}, on the left side and the coins in, {1, 4, 8, 9, 10, 12, 13, 14, 15, 18, 19, 21, 22, 28, 30, 32, 34, 37, 38, 39, 41, 42, 43, 44, 46, 52, 53, 54, 57, 60, 64, 66, 68, 69, 70, 71, 72, 74, 75, 79, 80, 162, 164, 166, 167, 170, 171, 173, 178, 179, 180, 181, 184, 185, 187, 188, 189, 190, 195, 198, 199, 200, 201, 202, 204, 206, 207, 210, 211, 216, 218, 221, 225, 228, 229, 234, 235, 236, 237, 239, 240, 242, 245, 248, 251, 253, 254, 255, 257, 262, 265, 266, 267, 270, 271, 273, 274, 275, 276, 280, 281, 282, 283, 286, 288, 289, 292, 293, 295, 296, 298, 301, 303, 305, 306, 312, 316, 317, 318, 320, 321}, on the right side In weighing number, 3, place the coins in , {2, 3, 5, 6, 7, 11, 16, 17, 20, 23, 24, 25, 26, 54, 57, 60, 64, 66, 68, 69, 70, 71, 72, 74, 75, 79, 80, 81, 83, 86, 88, 93, 94, 96, 97, 99, 101, 102, 138, 143, 144, 145, 146, 151, 152, 153, 154, 156, 157, 158, 162, 164, 166, 167, 170, 171, 173, 178, 179, 180, 181, 184, 185, 187, 188, 217, 219, 220, 222, 223, 224, 226, 227, 230, 231, 232, 233, 238, 241, 243, 244, 246, 247, 249, 250, 252, 256, 258, 259, 260, 261, 263, 264, 268, 269, 298, 301, 303, 305, 306, 312, 316, 317, 318, 320, 321, 325, 326, 328, 330, 331, 332, 333, 339, 340, 341, 343, 344, 345, 347, 349}, on the left side and the coins in, {1, 4, 8, 9, 10, 12, 13, 14, 15, 18, 19, 21, 22, 55, 56, 58, 59, 61, 62, 63, 65, 67, 73, 76, 77, 78, 82, 84, 85, 87, 89, 90, 91, 92, 95, 98, 100, 103, 104, 105, 106, 107, 135, 136, 137, 139, 140, 141, 142, 147, 148, 149, 150, 155, 159, 160, 161, 163, 165, 168, 169, 172, 174, 175, 176, 177, 182, 183, 186, 216, 218, 221, 225, 228, 229, 234, 235, 236, 237, 239, 240, 242, 245, 248, 251, 253, 254, 255, 257, 262, 265, 266, 267, 297, 299, 300, 302, 304, 307, 308, 309, 310, 311, 313, 314, 315, 319, 322, 323, 324, 327, 329, 334, 335, 336, 337, 338, 342, 346, 348, 350}, on the right side In weighing number, 4, place the coins in , {2, 3, 5, 6, 7, 18, 19, 21, 22, 27, 29, 31, 33, 35, 46, 52, 53, 55, 56, 58, 59, 61, 62, 72, 74, 75, 79, 80, 81, 83, 86, 88, 100, 103, 104, 105, 106, 107, 109, 111, 113, 115, 127, 128, 135, 136, 137, 139, 140, 141, 142, 153, 154, 156, 157, 158, 162, 164, 166, 167, 170, 182, 183, 186, 189, 190, 195, 208, 209, 212, 213, 214, 215, 216, 218, 221, 238, 241, 243, 244, 246, 247, 249, 250, 262, 265, 266, 267, 272, 277, 278, 288, 289, 292, 293, 295, 296, 297, 299, 300, 302, 304, 316, 317, 318, 320, 321, 325, 326, 328, 330, 331, 332, 342, 346, 348, 350, 351, 352, 355, 358}, on the left side and the coins in, {1, 4, 8, 20, 23, 24, 25, 26, 28, 30, 32, 34, 45, 47, 48, 49, 50, 51, 54, 57, 60, 73, 76, 77, 78, 82, 84, 85, 87, 89, 99, 101, 102, 108, 110, 112, 114, 116, 126, 129, 130, 131, 132, 133, 134, 138, 143, 155, 159, 160, 161, 163, 165, 168, 169, 180, 181, 184, 185, 187, 188, 191, 192, 193, 194, 196, 197, 207, 210, 211, 217, 219, 220, 222, 223, 224, 234, 235, 236, 237, 239, 240, 242, 245, 248, 251, 261, 263, 264, 268, 269, 270, 271, 273, 274, 275, 276, 290, 291, 294, 298, 301, 303, 305, 315, 319, 322, 323, 324, 327, 329, 343, 344, 345, 347, 349, 353, 354, 356, 357, 359}, on the right side In weighing number, 5, place the coins in , {2, 8, 11, 15, 20, 27, 29, 34, 36, 42, 43, 44, 45, 47, 52, 53, 55, 56, 60, 63, 65, 69, 70, 71, 73, 79, 80, 81, 83, 87, 89, 98, 99, 101, 105, 106, 107, 109, 114, 116, 119, 124, 126, 135, 136, 137, 143, 151, 152, 155, 162, 164, 168, 169, 171, 173, 177, 180, 181, 186, 189, 190, 196, 197, 198, 199, 200, 205, 207, 213, 214, 215, 216, 218, 222, 223, 224, 225, 231, 232, 233, 234, 235, 236, 241, 243, 244, 251, 252, 261, 263, 267, 272, 276, 279, 286, 290, 295, 296, 297, 299, 303, 305, 307, 308, 312, 315, 321, 325, 326, 333, 343, 344, 348, 350, 351, 352, 357, 359, 361, 362}, on the left side and the coins in, {1, 6, 7, 9, 10, 16, 17, 18, 19, 24, 25, 26, 28, 33, 35, 37, 38, 46, 51, 54, 61, 62, 64, 72, 74, 78, 82, 88, 90, 91, 92, 96, 97, 100, 108, 110, 115, 117, 118, 123, 125, 127, 128, 132, 133, 134, 141, 142, 144, 145, 146, 150, 153, 154, 159, 160, 161, 163, 170, 172, 178, 179, 182, 187, 188, 191, 195, 204, 206, 208, 209, 217, 226, 227, 240, 242, 245, 249, 250, 253, 254, 258, 259, 260, 262, 268, 269, 270, 271, 277, 278, 280, 281, 285, 287, 288, 289, 294, 298, 304, 306, 313, 314, 316, 317, 322, 323, 324, 330, 331, 332, 334, 335, 339, 340, 341, 342, 349, 353, 358, 360}, on the right side In weighing number, 6, place the coins in , {3, 6, 8, 14, 24, 27, 32, 33, 36, 38, 41, 44, 45, 48, 51, 53, 63, 68, 71, 74, 78, 80, 81, 89, 92, 93, 95, 96, 98, 99, 102, 104, 107, 110, 111, 116, 122, 123, 126, 128, 129, 132, 135, 141, 143, 146, 147, 150, 152, 158, 159, 162, 171, 176, 180, 182, 189, 191, 194, 195, 197, 198, 201, 203, 204, 207, 209, 210, 212, 215, 216, 224, 225, 227, 228, 230, 233, 234, 237, 240, 243, 245, 246, 248, 249, 251, 252, 254, 257, 258, 261, 264, 266, 275, 279, 281, 285, 291, 293, 294, 296, 297, 300, 305, 309, 315, 317, 320, 329, 330, 333, 335, 338, 339, 345, 350, 351, 353, 356, 359, 363}, on the left side and the coins in, {2, 5, 9, 11, 12, 15, 17, 18, 20, 21, 23, 26, 29, 30, 35, 39, 42, 47, 50, 54, 56, 57, 59, 60, 62, 65, 66, 69, 72, 75, 77, 83, 84, 86, 87, 90, 101, 105, 108, 113, 114, 117, 119, 120, 125, 131, 134, 137, 138, 140, 144, 149, 153, 155, 156, 161, 164, 165, 167, 168, 170, 173, 174, 177, 179, 183, 185, 186, 188, 192, 200, 206, 213, 218, 219, 221, 222, 231, 236, 239, 242, 255, 260, 263, 267, 269, 270, 272, 273, 276, 278, 282, 284, 287, 288, 290, 299, 302, 303, 306, 308, 311, 312, 314, 318, 321, 323, 324, 326, 327, 332, 336, 341, 342, 344, 347, 348, 354, 357, 360, 362}, on the right side