There should be 57 cards - To make it interesting they omitted two cards. Here is the complete list of 57 cards . Between any two cards there is exactly one common number - [In mathematical parlance it is projective plane of order 7,2] - To make kid friendly (and interesting, they substituted images/icons for numbers - If count the number of distinct images you ill see 57 in total] - Hope I answered your questions properly. Thanks again for suggesting people to look at this fascinating ("block design" or "projective plane" based) game
[[1, 2, 3, 4, 5, 6, 7, 8], [1, 9, 10, 11, 12, 13, 14, 15],
[1, 16, 27, 28, 29, 30, 31, 32], [1, 17, 22, 33, 42, 43, 44, 45],
[1, 18, 23, 37, 41, 51, 55, 57], [1, 19, 24, 34, 38, 47, 52, 56],
[1, 20, 25, 35, 39, 46, 50, 54], [1, 21, 26, 36, 40, 48, 49, 53],
[2, 9, 16, 17, 18, 19, 20, 21], [2, 10, 27, 33, 34, 35, 36, 37],
[2, 11, 23, 28, 42, 46, 47, 48], [2, 12, 22, 32, 40, 51, 54, 56],
[2, 13, 24, 29, 39, 44, 53, 55], [2, 14, 26, 30, 38, 43, 50, 57],
[2, 15, 25, 31, 41, 45, 49, 52], [3, 9, 28, 33, 38, 39, 40, 41],
[4, 9, 24, 27, 42, 49, 50, 51], [5, 9, 22, 31, 35, 47, 53, 57],
[6, 9, 23, 30, 36, 44, 52, 54], [7, 9, 25, 29, 37, 43, 48, 56],
[8, 9, 26, 32, 34, 45, 46, 55], [3, 10, 16, 22, 23, 24, 25, 26],
[3, 12, 18, 27, 43, 46, 52, 53], [3, 13, 19, 30, 35, 45, 48, 51],
[3, 11, 17, 31, 36, 50, 55, 56], [3, 15, 21, 29, 34, 42, 54, 57],
[3, 14, 20, 32, 37, 44, 47, 49], [5, 10, 19, 28, 43, 49, 54, 55],
[6, 10, 18, 29, 40, 45, 47, 50], [4, 10, 17, 32, 39, 48, 52, 57],
[8, 10, 20, 30, 41, 42, 53, 56], [7, 10, 21, 31, 38, 44, 46, 51],
[6, 13, 16, 33, 46, 49, 56, 57], [5, 12, 16, 34, 41, 44, 48, 50],
[4, 11, 16, 37, 38, 45, 53, 54], [8, 15, 16, 36, 39, 43, 47, 51],
[7, 14, 16, 35, 40, 42, 52, 55], [6, 14, 17, 25, 28, 34, 51, 53],
[4, 15, 18, 26, 28, 35, 44, 56], [7, 12, 20, 24, 28, 36, 45, 57],
[8, 13, 21, 22, 28, 37, 50, 52], [5, 14, 21, 23, 27, 39, 45, 56],
[6, 15, 20, 22, 27, 38, 48, 55], [7, 13, 17, 26, 27, 41, 47, 54],
[8, 11, 19, 25, 27, 40, 44, 57], [5, 11, 20, 26, 29, 33, 51, 52],
[4, 12, 21, 25, 30, 33, 47, 55], [8, 14, 18, 24, 31, 33, 48, 54],
[7, 15, 19, 23, 32, 33, 50, 53], [5, 13, 18, 25, 32, 36, 38, 42],
[5, 15, 17, 24, 30, 37, 40, 46], [6, 12, 19, 26, 31, 37, 39, 42],
[6, 11, 21, 24, 32, 35, 41, 43], [4, 13, 20, 23, 31, 34, 40, 43],
[4, 14, 19, 22, 29, 36, 41, 46], [8, 12, 17, 23, 29, 35, 38, 49],
[7, 11, 18, 22, 30, 34, 39, 49]]