SageMath, ProjectiveGeometryDesign, finite plane geometry, Dobble, Spot It

card-creation-dobble.md

Making cards is described in a few places and there are some samples of the output in stackoverflow.
I did a more thorough run through of one of the examples and put the output on this page for reference.

https://stackoverflow.com/a/31154452/999943

https://puzzlewocky.com/games/the-math-of-spot-it/

https://en.wikipedia.org/wiki/Dobble

incidence_matrix-output.txt

prime value: 2
card count: 7
[[0, 2, 5], [1, 4, 5], [0, 3, 4], [2, 4, 6], [1, 2, 3], [0, 1, 6], [3, 5, 6]]
---------
prime value: 3
card count: 13
[[0, 2, 9, 12], [3, 5, 7, 9], [0, 4, 7, 10], [1, 6, 9, 10], [2, 5, 10, 11], [1, 4, 5, 12], [3, 8, 10, 12], [1, 2, 7, 8], [6, 7, 11, 12], [0, 1, 3, 11], [2, 3, 4, 6], [4, 8, 9, 11], [0, 5, 6, 8]]
---------
prime value: 5
card count: 31
[[6, 7, 9, 18, 19, 29], [1, 4, 10, 14, 18, 26], [21, 22, 26, 27, 29, 30], [5, 14, 15, 17, 19, 21], [1, 8, 15, 23, 24, 29], [3, 5, 6, 16, 23, 26], [0, 5, 8, 18, 22, 25], [0, 9, 12, 15, 26, 28], [4, 6, 13, 15, 25, 27], [0, 7, 13, 14, 23, 30], [1, 12, 16, 19, 25, 30], [11, 12, 17, 18, 23, 27], [7, 10, 11, 15, 16, 22], [8, 9, 14, 16, 20, 27], [1, 3, 9, 13, 17, 22], [3, 4, 7, 8, 12, 21], [5, 10, 12, 13, 20, 29], [3, 11, 14, 25, 28, 29], [0, 1, 6, 11, 20, 21], [0, 3, 10, 19, 24, 27], [13, 16, 18, 21, 24, 28], [2, 3, 15, 18, 20, 30], [2, 6, 12, 14, 22, 24], [4, 5, 9, 11, 24, 30], [4, 19, 20, 22, 23, 28], [6, 8, 10, 17, 28, 30], [1, 2, 5, 7, 27, 28], [2, 8, 11, 13, 19, 26], [7, 17, 20, 24, 25, 26], [0, 2, 4, 16, 17, 29], [2, 9, 10, 21, 23, 25]]
---------
prime value: 7
card count: 57
[[27, 33, 36, 39, 40, 48, 49, 55], [15, 17, 19, 20, 34, 37, 53, 55], [2, 9, 34, 41, 44, 46, 49, 56], [15, 16, 18, 35, 36, 38, 54, 56], [9, 10, 17, 23, 26, 29, 39, 54], [13, 24, 25, 27, 28, 29, 34, 35], [7, 16, 17, 21, 25, 31, 33, 46], [6, 8, 9, 31, 35, 42, 43, 55], [7, 12, 30, 34, 38, 39, 42, 50], [2, 4, 7, 13, 14, 45, 54, 55], [4, 12, 18, 29, 37, 40, 43, 46], [11, 22, 24, 26, 38, 46, 51, 55], [8, 10, 15, 28, 30, 45, 46, 48], [5, 9, 16, 24, 40, 45, 50, 53], [9, 14, 18, 20, 21, 22, 27, 30], [1, 3, 12, 17, 22, 35, 45, 49], [3, 6, 13, 20, 23, 36, 46, 50], [1, 4, 6, 15, 21, 24, 39, 41], [3, 10, 14, 24, 33, 37, 42, 56], [1, 27, 42, 46, 47, 52, 53, 54], [1, 14, 16, 23, 34, 43, 48, 51], [6, 14, 17, 28, 38, 40, 44, 47], [11, 14, 15, 29, 31, 49, 50, 52], [4, 16, 20, 26, 28, 32, 42, 49], [5, 11, 13, 17, 18, 41, 42, 48], [5, 6, 25, 30, 37, 49, 51, 54], [4, 11, 23, 30, 33, 35, 44, 53], [0, 5, 14, 19, 32, 35, 39, 46], [5, 12, 21, 23, 28, 52, 55, 56], [4, 5, 10, 22, 31, 34, 36, 47], [8, 12, 14, 25, 26, 36, 41, 53], [6, 7, 22, 29, 32, 48, 53, 56], [23, 27, 31, 32, 37, 38, 41, 45], [0, 6, 18, 26, 33, 34, 45, 52], [1, 2, 5, 8, 20, 29, 33, 38], [3, 5, 7, 15, 26, 27, 43, 44], [0, 3, 16, 29, 30, 41, 47, 55], [1, 10, 18, 25, 32, 44, 50, 55], [3, 8, 11, 21, 32, 34, 40, 54], [0, 4, 8, 17, 27, 50, 51, 56], [0, 10, 13, 21, 38, 43, 49, 53], [2, 17, 24, 30, 32, 36, 43, 52], [7, 8, 18, 19, 23, 24, 47, 49], [7, 10, 20, 35, 40, 41, 51, 52], [2, 21, 26, 35, 37, 47, 48, 50], [9, 12, 13, 15, 32, 33, 47, 51], [2, 6, 10, 11, 12, 16, 19, 27], [19, 21, 29, 36, 42, 44, 45, 51], [0, 12, 20, 24, 31, 44, 48, 54], [0, 2, 15, 22, 23, 25, 40, 42], [8, 13, 16, 22, 37, 39, 44, 52], [11, 20, 25, 39, 43, 45, 47, 56], [19, 22, 28, 33, 41, 43, 50, 54], [1, 13, 19, 26, 30, 31, 40, 56], [3, 4, 9, 19, 25, 38, 48, 52], [0, 1, 7, 9, 11, 28, 36, 37], [2, 3, 18, 28, 31, 39, 51, 53]]
---------
prime value: 9
card count: 96
[[4, 14, 23, 35, 36, 38, 46, 57, 67, 69, 78, 80], [9, 14, 24, 33, 34, 36, 43, 60, 70, 71, 75, 95], [4, 12, 14, 27, 34, 61, 75, 81], [11, 14, 20, 33, 39, 42, 57, 61, 63, 86, 92], [0, 2, 4, 5, 6, 12, 14, 15, 19, 23, 25, 27, 28, 30, 34, 35, 38, 39, 47, 48, 50, 52, 59, 61, 62, 63, 64, 66, 75, 81, 82, 85, 86, 87, 89], [4, 14, 27, 53, 61, 75], [4, 6, 7, 14, 20, 41, 68, 70, 79, 87, 89, 90], [6, 11, 14, 19, 27, 29, 36, 40, 49, 64, 76, 94], [14, 31, 38, 45, 53, 54, 61, 62, 70, 76, 85, 93], [1, 10, 14, 19, 24, 53, 58, 61, 66, 73, 80, 89], [9, 14, 29, 32, 38, 51, 61, 62, 74, 79, 85], [3, 7, 14, 17, 23, 27, 37, 42, 62, 73, 82, 95], [2, 4, 14, 18, 50, 60, 63, 72, 73, 74, 76, 88], [14, 20, 26, 27, 35, 37, 47, 65, 73, 77, 85, 95], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95], [4, 14, 17, 32, 43, 45, 52, 64, 66, 77, 90, 92], [14, 21, 29, 41, 42, 54, 56, 75, 77, 80, 81, 88], [11, 14, 15, 26, 27, 31, 36, 51, 52, 88, 89, 94], [12, 14, 23, 25, 28, 30, 59, 63, 64, 75, 85, 89], [4, 7, 9, 14, 20, 41, 52, 64, 66, 67, 91, 93], [3, 6, 13, 14, 19, 27, 31, 51, 57, 64, 71, 88], [14, 16, 38, 40, 43, 61, 62, 68, 85, 88, 91], [14, 22, 33, 36, 45, 71, 73, 75, 79, 81, 83, 91], [0, 4, 11, 14, 18, 69, 71, 78, 80, 82, 84, 85], [1, 9, 14, 37, 43, 57, 70, 72, 75, 81, 84, 94], [4, 14, 18, 27, 61, 67, 75, 90], [13, 14, 17, 36, 39, 41, 61, 63, 65, 84, 86], [2, 4, 5, 7, 11, 13, 14, 17, 20, 25, 27, 28, 33, 36, 39, 41, 42, 46, 48, 50, 53, 55, 57, 61, 63, 65, 71, 75, 77, 84, 86, 92, 94], [4, 14, 18, 27, 61, 67, 75, 90], [7, 10, 14, 16, 44, 51, 65, 75, 76, 78, 81, 92], [4, 14, 18, 42, 52, 55, 64, 65, 66, 68, 70, 79], [8, 14, 17, 20, 31, 40, 55, 58, 69, 74, 75, 81], [10, 14, 15, 37, 58, 60, 61, 64, 80, 83, 87], [1, 3, 14, 22, 27, 35, 41, 47, 55, 60, 85, 92], [1, 2, 4, 14, 40, 50, 51, 54, 63, 67, 83, 95], [0, 4, 13, 14, 33, 44, 56, 58, 67, 82, 85, 94], [0, 1, 7, 14, 17, 22, 26, 27, 38, 42, 59, 60], [11, 13, 14, 24, 32, 46, 60, 68, 75, 81, 93, 95], [0, 4, 8, 10, 14, 21, 36, 46, 57, 82, 85, 90], [3, 4, 14, 26, 27, 49, 61, 75], [7, 14, 21, 31, 34, 40, 56, 65, 74, 75, 80, 92], [6, 14, 16, 19, 26, 27, 33, 46, 54, 64, 74, 84], [3, 11, 14, 16, 27, 30, 36, 54, 66, 74, 87, 94], [1, 14, 15, 21, 24, 44, 61, 64, 69, 73, 87], [14, 29, 35, 43, 51, 53, 59, 61, 68, 74, 82, 91], [8, 14, 15, 22, 53, 56, 61, 64, 72, 78, 87, 95], [0, 14, 27, 37, 38, 41, 49, 55, 59, 73, 92, 95], [4, 13, 14, 33, 47, 59, 62, 69, 78, 80, 90, 94], [4, 14, 27, 53, 61, 75], [7, 14, 39, 46, 53, 55, 61, 63, 71, 77, 86, 94], [4, 12, 14, 27, 34, 61, 75, 81], [10, 14, 17, 20, 29, 34, 44, 54, 55, 75, 78, 88], [4, 14, 15, 17, 19, 30, 67, 68, 70, 77, 79, 92], [5, 8, 9, 14, 27, 44, 45, 48, 49, 63, 68, 80], [8, 14, 16, 34, 41, 42, 51, 58, 69, 75, 76, 77], [14, 27, 30, 31, 33, 46, 49, 51, 66, 84, 87, 88], [14, 16, 35, 40, 45, 59, 61, 70, 82, 88, 93], [0, 3, 14, 20, 24, 27, 38, 59, 65, 72, 77, 83], [9, 14, 31, 32, 35, 54, 59, 61, 76, 79, 82], [4, 14, 18, 36, 44, 46, 47, 56, 57, 58, 59, 62], [1, 12, 14, 32, 33, 36, 37, 68, 71, 72, 75, 93], [2, 3, 4, 5, 8, 9, 10, 14, 21, 25, 26, 27, 28, 32, 39, 43, 44, 45, 48, 49, 50, 56, 58, 61, 63, 68, 69, 70, 75, 78, 79, 80, 86, 91, 93], [4, 8, 10, 11, 14, 21, 47, 59, 62, 67, 71, 84], [3, 4, 12, 14, 18, 26, 27, 34, 49, 53, 61, 67, 75, 81, 90], [4, 7, 14, 15, 18, 19, 20, 30, 32, 41, 43, 45], [13, 14, 26, 27, 29, 30, 40, 57, 66, 71, 76, 87], [4, 9, 14, 15, 19, 30, 42, 55, 65, 90, 91, 93], [0, 14, 19, 25, 28, 34, 35, 52, 62, 63, 75, 87], [6, 14, 21, 30, 37, 44, 52, 53, 60, 61, 69, 83], [0, 14, 23, 31, 43, 47, 54, 61, 68, 76, 91], [1, 6, 8, 14, 24, 30, 52, 56, 61, 73, 78], [1, 14, 20, 22, 23, 27, 49, 60, 62, 65, 77, 82], [12, 14, 24, 45, 57, 60, 75, 79, 84, 91, 94, 95], [9, 11, 12, 13, 14, 22, 43, 46, 70, 73, 75, 83], [10, 12, 14, 31, 40, 41, 42, 44, 74, 75, 77, 78], [1, 2, 4, 5, 14, 16, 18, 22, 24, 25, 27, 28, 29, 31, 37, 39, 40, 48, 50, 51, 54, 60, 61, 63, 67, 72, 73, 74, 75, 76, 83, 86, 88, 90, 95], [7, 8, 12, 14, 29, 54, 58, 65, 69, 75, 88, 92], [13, 14, 15, 16, 27, 49, 52, 54, 57, 71, 74, 89], [0, 14, 23, 29, 45, 47, 51, 61, 70, 74, 93], [6, 10, 14, 22, 30, 52, 58, 61, 72, 80, 95], [0, 9, 14, 16, 23, 32, 40, 47, 53, 61, 79, 88], [2, 4, 14, 16, 22, 24, 29, 31, 37, 50, 63, 90], [4, 11, 14, 23, 35, 38, 44, 56, 58, 71, 84, 90], [14, 22, 32, 34, 57, 68, 73, 75, 83, 84, 93, 94], [14, 23, 24, 26, 27, 41, 55, 62, 72, 82, 83, 92], [4, 8, 10, 13, 14, 18, 21, 23, 33, 35, 38, 94], [3, 4, 14, 26, 27, 49, 61, 75], [4, 6, 14, 32, 42, 43, 45, 55, 65, 67, 87, 89], [12, 14, 16, 17, 20, 21, 51, 55, 56, 75, 76, 80], [4, 6, 9, 14, 17, 18, 77, 87, 89, 91, 92, 93], [6, 14, 15, 25, 28, 38, 47, 63, 66, 75, 81, 82], [14, 19, 21, 22, 44, 61, 66, 69, 72, 89, 95], [3, 14, 15, 27, 29, 33, 40, 46, 52, 76, 84, 89], [8, 14, 19, 37, 56, 60, 61, 66, 78, 83, 89], [7, 14, 17, 24, 27, 35, 42, 47, 49, 72, 83, 85], [1, 11, 13, 14, 34, 37, 45, 46, 72, 75, 79, 91]]
---------
prime value: 11
card count: 133
[[6, 19, 28, 29, 43, 51, 63, 74, 93, 114, 126, 132], [1, 4, 10, 19, 22, 24, 34, 40, 48, 54, 116, 131], [27, 28, 32, 34, 37, 39, 82, 87, 88, 118, 119, 124], [7, 10, 25, 26, 30, 63, 81, 82, 86, 97, 105, 117], [1, 13, 25, 33, 68, 73, 80, 90, 103, 112, 114, 124], [20, 28, 50, 52, 85, 89, 92, 94, 112, 116, 117, 121], [0, 10, 13, 23, 28, 44, 47, 56, 59, 72, 98, 109], [3, 13, 18, 29, 64, 81, 94, 108, 110, 118, 123, 131], [18, 21, 26, 28, 41, 48, 65, 68, 76, 96, 101, 102], [16, 28, 36, 45, 54, 67, 69, 73, 81, 91, 104, 125], [1, 3, 6, 17, 21, 66, 67, 82, 98, 100, 111, 121], [38, 46, 48, 56, 71, 73, 82, 93, 94, 106, 115, 127], [15, 22, 26, 39, 47, 69, 75, 84, 93, 103, 110, 121], [4, 6, 7, 15, 50, 56, 68, 78, 79, 87, 123, 125], [38, 43, 60, 78, 81, 96, 103, 109, 111, 113, 116, 119], [12, 13, 21, 31, 38, 39, 54, 55, 79, 85, 86, 126], [9, 16, 18, 40, 42, 70, 75, 79, 82, 92, 109, 114], [10, 18, 37, 53, 61, 62, 84, 106, 111, 112, 125, 126], [7, 8, 16, 17, 34, 59, 94, 95, 102, 103, 122, 126], [0, 1, 20, 30, 45, 64, 75, 87, 96, 107, 126, 127], [5, 19, 30, 44, 52, 62, 67, 79, 101, 103, 115, 118], [8, 10, 15, 21, 43, 52, 57, 70, 91, 108, 124, 127], [1, 12, 23, 35, 50, 62, 70, 76, 81, 88, 93, 95], [6, 22, 31, 33, 41, 44, 45, 53, 70, 94, 97, 119], [1, 27, 42, 43, 47, 49, 86, 94, 101, 125, 129, 130], [3, 4, 53, 63, 69, 71, 85, 95, 101, 107, 109, 124], [3, 8, 12, 30, 40, 47, 68, 89, 104, 106, 119, 132], [2, 24, 28, 70, 83, 86, 100, 103, 106, 107, 120, 123], [0, 2, 5, 6, 8, 9, 27, 48, 81, 84, 85, 90], [0, 7, 39, 46, 66, 70, 74, 101, 104, 112, 113, 131], [3, 19, 20, 26, 32, 38, 58, 59, 70, 77, 90, 125], [15, 23, 32, 49, 67, 85, 96, 97, 106, 114, 122, 131], [2, 30, 31, 60, 92, 93, 98, 102, 124, 125, 128, 131], [4, 23, 41, 52, 60, 82, 83, 90, 104, 110, 126, 130], [1, 2, 18, 52, 55, 56, 69, 74, 77, 105, 119, 122], [22, 56, 61, 66, 86, 90, 91, 92, 95, 96, 118, 132], [9, 36, 47, 66, 76, 77, 97, 115, 116, 123, 124, 126], [2, 17, 38, 40, 44, 49, 63, 76, 87, 91, 110, 112], [11, 14, 15, 30, 37, 54, 74, 76, 90, 94, 100, 109], [2, 12, 15, 29, 45, 59, 61, 80, 82, 99, 101, 116], [1, 16, 26, 37, 44, 46, 57, 60, 85, 99, 123, 132], [8, 23, 33, 46, 55, 63, 65, 75, 100, 116, 118, 125], [16, 24, 55, 72, 87, 89, 90, 93, 97, 101, 108, 111], [0, 14, 21, 24, 95, 99, 110, 114, 115, 117, 119, 125], [6, 20, 23, 37, 40, 69, 80, 86, 102, 108, 113, 115], [9, 19, 23, 39, 68, 91, 94, 99, 105, 107, 111, 128], [11, 29, 40, 41, 66, 72, 85, 88, 103, 105, 125, 127], [6, 12, 24, 26, 36, 109, 112, 118, 122, 127, 128, 130], [1, 8, 11, 28, 58, 61, 71, 79, 97, 110, 113, 128], [24, 31, 37, 49, 51, 52, 59, 66, 68, 71, 75, 81], [5, 13, 22, 51, 57, 76, 82, 89, 107, 113, 122, 125], [0, 49, 50, 53, 54, 65, 77, 82, 103, 108, 128, 132], [5, 20, 21, 33, 34, 49, 61, 93, 104, 105, 109, 123], [17, 23, 25, 51, 54, 58, 84, 92, 101, 119, 123, 127], [1, 9, 15, 38, 51, 53, 72, 102, 104, 117, 118, 120], [15, 34, 41, 42, 55, 58, 81, 98, 107, 112, 115, 132], [6, 11, 13, 34, 35, 60, 75, 77, 91, 101, 106, 117], [21, 40, 50, 59, 60, 73, 74, 84, 97, 107, 118, 129], [30, 48, 53, 55, 59, 88, 91, 113, 114, 121, 123, 130], [6, 18, 30, 39, 49, 57, 58, 72, 73, 83, 95, 116], [14, 32, 33, 40, 56, 57, 81, 101, 120, 121, 126, 128], [17, 35, 39, 48, 52, 64, 80, 97, 109, 120, 125, 132], [17, 20, 22, 65, 72, 74, 79, 81, 99, 106, 124, 130], [0, 3, 25, 37, 41, 79, 91, 93, 116, 120, 122, 129], [7, 19, 61, 73, 75, 76, 85, 98, 108, 119, 120, 130], [8, 41, 51, 62, 73, 77, 86, 87, 99, 109, 121, 131], [10, 29, 35, 36, 46, 49, 79, 90, 102, 107, 119, 121], [9, 10, 20, 31, 73, 78, 88, 100, 101, 110, 122, 132], [4, 8, 13, 26, 45, 49, 74, 88, 92, 111, 115, 120], [9, 12, 25, 34, 44, 71, 74, 83, 96, 108, 121, 125], [16, 21, 22, 23, 27, 29, 30, 71, 77, 78, 112, 120], [11, 25, 48, 49, 69, 70, 78, 89, 98, 99, 118, 126], [6, 42, 46, 54, 59, 62, 89, 96, 105, 110, 120, 124], [4, 9, 11, 57, 59, 64, 65, 67, 86, 93, 112, 119], [0, 29, 34, 38, 57, 62, 68, 69, 92, 97, 100, 130], [12, 16, 19, 41, 49, 56, 64, 84, 100, 113, 117, 124], [8, 22, 36, 37, 38, 50, 64, 83, 98, 101, 105, 114], [30, 34, 36, 51, 56, 65, 70, 80, 85, 110, 111, 129], [13, 14, 67, 70, 71, 84, 87, 102, 105, 116, 130, 132], [13, 15, 16, 20, 48, 62, 63, 66, 83, 119, 128, 129], [4, 39, 44, 61, 77, 81, 89, 100, 102, 114, 127, 129], [3, 7, 9, 14, 22, 28, 49, 55, 60, 62, 80, 127], [2, 3, 10, 11, 16, 33, 39, 50, 51, 96, 115, 130], [27, 33, 59, 69, 76, 79, 83, 111, 117, 127, 131, 132], [12, 17, 28, 53, 57, 75, 78, 90, 105, 115, 129, 131], [5, 15, 25, 28, 31, 40, 46, 64, 77, 95, 111, 130], [3, 15, 24, 27, 35, 44, 65, 73, 92, 105, 113, 126], [2, 13, 19, 37, 42, 65, 78, 95, 97, 104, 121, 127], [2, 22, 46, 58, 67, 68, 88, 108, 109, 117, 126, 129], [5, 26, 42, 50, 71, 72, 80, 91, 100, 119, 126, 131], [4, 28, 30, 33, 35, 38, 42, 66, 84, 99, 108, 122], [9, 21, 35, 37, 45, 56, 58, 63, 89, 103, 130, 131], [5, 16, 32, 35, 53, 68, 74, 86, 98, 110, 116, 127], [0, 11, 12, 22, 32, 42, 52, 63, 73, 102, 111, 123], [5, 7, 11, 18, 23, 24, 38, 45, 121, 124, 129, 132], [18, 22, 25, 35, 43, 59, 85, 87, 100, 104, 115, 128], [8, 14, 19, 31, 35, 69, 72, 82, 96, 112, 123, 129], [3, 23, 31, 36, 42, 48, 57, 61, 74, 87, 103, 117], [6, 10, 32, 55, 64, 71, 76, 92, 99, 103, 104, 129], [39, 40, 43, 45, 62, 65, 71, 90, 98, 117, 122, 123], [10, 27, 38, 41, 67, 74, 75, 80, 89, 95, 123, 128], [8, 20, 24, 25, 29, 39, 42, 53, 56, 60, 67, 76], [8, 18, 32, 44, 54, 66, 78, 80, 93, 107, 117, 130], [4, 12, 14, 18, 20, 27, 46, 51, 91, 97, 98, 103], [9, 26, 29, 33, 52, 54, 87, 95, 98, 106, 113, 129], [3, 34, 45, 46, 52, 72, 76, 78, 84, 86, 114, 128], [11, 17, 26, 27, 31, 56, 62, 104, 107, 108, 114, 116], [19, 25, 27, 45, 50, 55, 57, 66, 102, 106, 109, 110], [7, 21, 42, 44, 51, 64, 69, 88, 90, 106, 116, 128], [6, 14, 16, 25, 38, 47, 52, 61, 65, 88, 107, 131], [7, 12, 33, 37, 43, 48, 67, 72, 77, 92, 107, 110], [10, 14, 17, 42, 45, 68, 77, 83, 85, 93, 113, 118], [4, 5, 17, 29, 37, 47, 55, 70, 73, 96, 117, 128], [14, 29, 44, 48, 50, 58, 75, 86, 104, 111, 122, 124], [0, 4, 16, 31, 43, 58, 76, 80, 105, 106, 118, 121], [11, 20, 36, 43, 44, 55, 68, 82, 84, 95, 120, 131], [1, 5, 14, 36, 39, 41, 59, 63, 78, 92, 106, 108], [3, 5, 43, 54, 56, 75, 83, 88, 97, 99, 102, 112], [2, 7, 20, 35, 41, 47, 54, 57, 71, 111, 114, 118], [2, 14, 23, 26, 34, 43, 53, 64, 66, 73, 79, 89], [27, 54, 60, 61, 63, 64, 68, 70, 72, 115, 121, 122], [5, 10, 12, 58, 60, 65, 66, 69, 87, 94, 114, 120], [18, 31, 34, 47, 50, 63, 67, 90, 99, 113, 120, 127], [7, 13, 27, 36, 40, 52, 53, 58, 93, 96, 99, 100], [2, 4, 21, 25, 32, 36, 62, 72, 75, 94, 113, 132], [9, 13, 17, 24, 30, 32, 41, 43, 46, 50, 61, 69], [0, 15, 17, 18, 19, 33, 36, 60, 71, 86, 88, 89], [11, 19, 21, 46, 47, 53, 80, 81, 83, 87, 92, 122], [32, 45, 47, 48, 51, 60, 79, 95, 100, 105, 108, 112], [24, 57, 63, 77, 79, 80, 84, 88, 94, 96, 98, 104], [24, 33, 47, 58, 62, 64, 74, 78, 82, 85, 91, 102], [1, 7, 29, 31, 32, 65, 83, 84, 89, 91, 109, 115], [0, 26, 35, 40, 51, 55, 61, 67, 78, 83, 94, 124]]
---------

incidence_matrix.py

# https://stackoverflow.com/a/51464741/999943
def incidence_matrix(p = 7): # p can be any prime

    # Generate all p^3 - 1 points in affine space, minus the origin:
    points = [(a,b,c) for a in range(p) for b in range(p) for c in range(p)][1::]

    # Quotient by the equivalence relation to give the projective plane points:
    scale = lambda t, k : tuple([((k * v) % p) for v in t])
    canonise = lambda t : (sorted([scale(t, k) for k in range(1, p)])[0])
    points = list(set(map(canonise, points)))

    # We identify each point with its dual line by taking orthogonal complements.
    # A line is incident with a point if the pole of the line is orthogonal to
    # the point, which can be evaluated straightforwardly:
    innerprod = lambda x, y : (sum([a*b for (a, b) in zip(x, y)]) % p)
    imatrix = [[1 if (innerprod(x, y) == 0) else 0 for x in points] for y in points]

    # Output the incidence matrix:
    return imatrix

def indices_of_ones(row):
    return [i for i, value in enumerate(row) if value == 1]

for p in [2,3,5,7,11]:
    m = incidence_matrix(p)
    cards = [indices_of_ones(row) for row in m]
    print("prime value:", p)
    print("card count:", len(cards))
    print(cards)
    print("---------")

itertools-create-cards-output.txt

order: 2
count: 7
[{0, 1, 4}, {2, 3, 4}, {0, 2, 5}, {1, 3, 5}, {0, 3, 6}, {1, 2, 6}, {4, 5, 6}]
------------
order: 3
count: 13
[{0, 1, 2, 9}, {9, 3, 4, 5}, {8, 9, 6, 7}, {0, 10, 3, 6}, {1, 10, 4, 7}, {8, 2, 10, 5}, {0, 8, 11, 4}, {1, 11, 5, 6}, {11, 2, 3, 7}, {0, 12, 5, 7}, {8, 1, 3, 12}, {2, 4, 12, 6}, {9, 10, 11, 12}]
------------
order: 5
count: 31
[{0, 1, 2, 3, 4, 25}, {5, 6, 7, 8, 9, 25}, {10, 11, 12, 13, 14, 25}, {15, 16, 17, 18, 19, 25}, {20, 21, 22, 23, 24, 25}, {0, 5, 10, 15, 20, 26}, {1, 6, 11, 16, 21, 26}, {2, 7, 12, 17, 22, 26}, {3, 8, 13, 18, 23, 26}, {4, 9, 14, 19, 24, 26}, {0, 6, 12, 18, 24, 27}, {1, 7, 13, 19, 20, 27}, {2, 8, 14, 15, 21, 27}, {3, 9, 10, 16, 22, 27}, {4, 5, 11, 17, 23, 27}, {0, 7, 14, 16, 23, 28}, {1, 8, 10, 17, 24, 28}, {2, 9, 11, 18, 20, 28}, {3, 5, 12, 19, 21, 28}, {4, 6, 13, 15, 22, 28}, {0, 8, 11, 19, 22, 29}, {1, 9, 12, 15, 23, 29}, {2, 5, 13, 16, 24, 29}, {3, 6, 14, 17, 20, 29}, {4, 7, 10, 18, 21, 29}, {0, 9, 13, 17, 21, 30}, {1, 5, 14, 18, 22, 30}, {2, 6, 10, 19, 23, 30}, {3, 7, 11, 15, 24, 30}, {4, 8, 12, 16, 20, 30}, {25, 26, 27, 28, 29, 30}]
------------
order: 7
count: 57
[{0, 1, 2, 3, 4, 5, 6, 49}, {7, 8, 9, 10, 11, 12, 13, 49}, {14, 15, 16, 17, 18, 19, 20, 49}, {49, 21, 22, 23, 24, 25, 26, 27}, {32, 33, 34, 49, 28, 29, 30, 31}, {35, 36, 37, 38, 39, 40, 41, 49}, {42, 43, 44, 45, 46, 47, 48, 49}, {0, 35, 7, 42, 14, 50, 21, 28}, {1, 36, 8, 43, 15, 50, 22, 29}, {2, 37, 9, 44, 16, 50, 23, 30}, {3, 38, 10, 45, 17, 50, 24, 31}, {32, 4, 39, 11, 46, 18, 50, 25}, {33, 5, 40, 12, 47, 50, 19, 26}, {34, 6, 41, 13, 48, 50, 20, 27}, {0, 32, 8, 40, 16, 48, 51, 24}, {1, 33, 9, 41, 42, 17, 51, 25}, {2, 34, 35, 10, 43, 18, 51, 26}, {3, 36, 11, 44, 19, 51, 27, 28}, {4, 37, 12, 45, 51, 20, 21, 29}, {5, 38, 13, 14, 46, 51, 22, 30}, {6, 7, 39, 15, 47, 51, 23, 31}, {0, 38, 9, 47, 18, 52, 27, 29}, {1, 39, 10, 48, 19, 52, 21, 30}, {2, 40, 42, 11, 20, 52, 22, 31}, {32, 3, 41, 43, 12, 14, 52, 23}, {33, 35, 4, 44, 13, 15, 52, 24}, {34, 36, 5, 7, 45, 16, 52, 25}, {37, 6, 8, 46, 17, 52, 26, 28}, {0, 33, 36, 10, 46, 20, 53, 23}, {1, 34, 37, 11, 14, 47, 53, 24}, {2, 38, 12, 15, 48, 53, 25, 28}, {3, 39, 42, 13, 16, 53, 26, 29}, {4, 7, 40, 43, 17, 53, 27, 30}, {5, 8, 41, 44, 18, 21, 53, 31}, {32, 35, 6, 9, 45, 19, 53, 22}, {0, 41, 11, 45, 15, 54, 26, 30}, {1, 35, 12, 46, 16, 54, 27, 31}, {32, 2, 36, 13, 47, 17, 21, 54}, {33, 3, 37, 7, 48, 18, 22, 54}, {34, 4, 38, 8, 42, 19, 54, 23}, {5, 39, 9, 43, 20, 54, 24, 28}, {6, 40, 10, 44, 14, 54, 25, 29}, {0, 34, 39, 12, 44, 17, 22, 55}, {1, 40, 13, 45, 18, 55, 23, 28}, {2, 7, 41, 46, 19, 55, 24, 29}, {3, 35, 8, 47, 20, 55, 25, 30}, {4, 36, 9, 14, 48, 55, 26, 31}, {32, 5, 37, 10, 42, 15, 55, 27}, {33, 6, 38, 11, 43, 16, 21, 55}, {0, 37, 43, 13, 19, 56, 25, 31}, {32, 1, 38, 7, 44, 20, 56, 26}, {33, 2, 39, 8, 45, 14, 56, 27}, {34, 3, 40, 9, 46, 15, 21, 56}, {4, 41, 10, 47, 16, 22, 56, 28}, {35, 5, 11, 48, 17, 23, 56, 29}, {36, 6, 42, 12, 18, 24, 56, 30}, {49, 50, 51, 52, 53, 54, 55, 56}]
------------
order: 11
count: 133
[{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 121}, {11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 121}, {32, 121, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31}, {33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 121}, {44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 121}, {64, 65, 121, 55, 56, 57, 58, 59, 60, 61, 62, 63}, {66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 121}, {77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 121}, {96, 97, 98, 121, 88, 89, 90, 91, 92, 93, 94, 95}, {99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 121}, {110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121}, {0, 33, 66, 99, 11, 44, 77, 110, 22, 55, 88, 122}, {1, 34, 67, 100, 12, 45, 78, 111, 23, 56, 89, 122}, {2, 35, 68, 101, 122, 13, 46, 79, 112, 24, 57, 90}, {3, 36, 69, 102, 122, 14, 47, 80, 113, 25, 58, 91}, {4, 37, 70, 103, 122, 15, 48, 81, 114, 26, 59, 92}, {5, 38, 71, 104, 16, 49, 82, 115, 122, 27, 60, 93}, {6, 39, 72, 105, 17, 50, 83, 116, 122, 28, 61, 94}, {7, 40, 73, 106, 18, 51, 84, 117, 122, 29, 62, 95}, {96, 8, 41, 74, 107, 19, 52, 85, 118, 122, 30, 63}, {64, 97, 9, 42, 75, 108, 20, 53, 86, 119, 122, 31}, {32, 65, 98, 10, 43, 76, 109, 21, 54, 87, 120, 122}, {0, 96, 36, 72, 12, 108, 120, 48, 84, 24, 123, 60}, {1, 97, 37, 73, 13, 109, 110, 49, 85, 25, 123, 61}, {2, 98, 99, 38, 74, 14, 111, 50, 86, 26, 123, 62}, {3, 100, 39, 75, 123, 15, 112, 51, 87, 88, 27, 63}, {64, 4, 101, 40, 76, 77, 16, 113, 52, 89, 123, 28}, {65, 66, 5, 102, 41, 78, 17, 114, 53, 90, 123, 29}, {67, 6, 103, 42, 123, 79, 18, 115, 54, 55, 91, 30}, {68, 7, 104, 43, 44, 80, 19, 116, 56, 123, 92, 31}, {32, 33, 69, 8, 105, 45, 81, 20, 117, 57, 123, 93}, {34, 70, 9, 106, 46, 82, 21, 22, 118, 58, 123, 94}, {35, 71, 10, 11, 107, 123, 47, 83, 119, 23, 59, 95}, {0, 65, 67, 39, 106, 13, 80, 52, 119, 26, 124, 93}, {1, 68, 40, 107, 14, 81, 53, 55, 120, 27, 124, 94}, {2, 69, 41, 108, 110, 15, 124, 82, 54, 56, 28, 95}, {96, 3, 70, 42, 44, 109, 111, 16, 83, 57, 124, 29}, {97, 99, 4, 71, 43, 45, 112, 17, 84, 58, 124, 30}, {33, 98, 100, 5, 72, 46, 113, 18, 85, 59, 124, 31}, {32, 34, 101, 6, 73, 47, 124, 114, 19, 86, 88, 60}, {35, 102, 7, 74, 48, 115, 20, 22, 87, 89, 124, 61}, {36, 103, 8, 75, 77, 49, 116, 21, 23, 90, 124, 62}, {37, 104, 9, 11, 76, 78, 50, 117, 24, 91, 124, 63}, {64, 66, 38, 105, 10, 12, 79, 124, 51, 118, 25, 92}, {0, 104, 73, 42, 45, 14, 118, 87, 90, 59, 28, 125}, {1, 105, 74, 43, 77, 46, 15, 125, 119, 91, 60, 29}, {33, 2, 106, 75, 78, 47, 16, 125, 120, 92, 61, 30}, {34, 3, 107, 76, 110, 79, 48, 17, 125, 93, 62, 31}, {32, 66, 35, 4, 108, 111, 80, 49, 18, 125, 94, 63}, {64, 67, 36, 5, 109, 112, 81, 50, 19, 22, 125, 95}, {96, 65, 99, 68, 37, 6, 113, 82, 51, 20, 23, 125}, {97, 100, 69, 38, 7, 114, 83, 52, 21, 55, 24, 125}, {98, 101, 70, 39, 8, 11, 115, 84, 53, 56, 25, 125}, {102, 71, 40, 9, 12, 116, 85, 54, 88, 57, 26, 125}, {103, 72, 41, 10, 44, 13, 117, 86, 89, 58, 27, 125}, {0, 64, 34, 98, 68, 102, 15, 49, 83, 117, 126, 30}, {1, 65, 35, 69, 103, 16, 50, 84, 118, 88, 126, 31}, {32, 2, 36, 70, 104, 17, 51, 119, 85, 55, 89, 126}, {3, 37, 71, 105, 18, 52, 22, 86, 56, 90, 120, 126}, {4, 38, 72, 106, 110, 19, 53, 87, 23, 57, 91, 126}, {5, 39, 73, 107, 77, 111, 20, 54, 24, 58, 92, 126}, {6, 40, 74, 44, 108, 78, 112, 21, 25, 59, 93, 126}, {126, 7, 41, 11, 75, 45, 109, 79, 113, 26, 60, 94}, {99, 8, 42, 12, 76, 46, 80, 114, 27, 61, 126, 95}, {96, 66, 100, 9, 43, 13, 47, 81, 115, 126, 28, 62}, {33, 97, 67, 101, 10, 14, 48, 82, 116, 29, 126, 63}, {0, 32, 100, 37, 74, 79, 16, 116, 53, 58, 127, 95}, {96, 1, 101, 38, 75, 80, 17, 117, 54, 22, 59, 127}, {97, 2, 102, 39, 44, 76, 81, 18, 118, 23, 60, 127}, {66, 3, 98, 103, 40, 45, 82, 19, 119, 24, 61, 127}, {67, 4, 104, 41, 46, 83, 20, 88, 25, 120, 62, 127}, {68, 5, 105, 42, 110, 47, 84, 21, 89, 26, 127, 63}, {64, 69, 6, 106, 43, 11, 111, 48, 85, 90, 27, 127}, {33, 65, 70, 7, 107, 12, 112, 49, 86, 91, 28, 127}, {34, 71, 8, 108, 13, 113, 50, 87, 55, 92, 29, 127}, {35, 72, 9, 77, 14, 109, 114, 51, 56, 93, 30, 127}, {99, 36, 73, 10, 78, 15, 115, 52, 57, 127, 94, 31}, {0, 128, 69, 40, 109, 46, 17, 115, 86, 23, 92, 63}, {64, 1, 128, 99, 70, 41, 47, 18, 116, 87, 24, 93}, {128, 65, 2, 100, 71, 42, 77, 48, 19, 117, 25, 94}, {128, 3, 101, 72, 43, 78, 49, 20, 118, 55, 26, 95}, {96, 33, 128, 4, 102, 73, 79, 50, 21, 119, 56, 27}, {128, 97, 34, 5, 103, 74, 11, 80, 51, 120, 57, 28}, {128, 98, 35, 6, 104, 75, 12, 110, 81, 52, 58, 29}, {128, 36, 7, 105, 76, 13, 111, 82, 53, 88, 59, 30}, {128, 66, 37, 8, 106, 14, 112, 83, 54, 89, 60, 31}, {32, 128, 67, 38, 9, 107, 44, 15, 113, 84, 90, 61}, {128, 68, 39, 10, 108, 45, 16, 114, 85, 22, 91, 62}, {0, 89, 129, 43, 75, 107, 18, 50, 82, 114, 25, 57}, {1, 33, 129, 58, 90, 76, 108, 19, 51, 83, 115, 26}, {129, 2, 34, 66, 59, 91, 109, 20, 52, 84, 116, 27}, {129, 35, 3, 67, 99, 60, 92, 53, 21, 85, 117, 28}, {129, 4, 36, 68, 100, 11, 61, 93, 54, 86, 118, 29}, {129, 37, 5, 69, 101, 12, 44, 119, 87, 62, 94, 30}, {129, 38, 6, 70, 102, 45, 13, 77, 120, 63, 95, 31}, {32, 64, 96, 129, 39, 7, 71, 103, 46, 14, 78, 110}, {65, 97, 129, 8, 40, 72, 104, 47, 15, 79, 111, 22}, {129, 98, 9, 41, 73, 105, 16, 48, 80, 112, 55, 23}, {129, 10, 42, 74, 106, 17, 49, 81, 113, 24, 56, 88}, {0, 97, 130, 35, 70, 105, 78, 113, 19, 54, 27, 62}, {1, 98, 130, 36, 71, 106, 44, 79, 114, 20, 28, 63}, {64, 2, 130, 37, 72, 107, 45, 80, 115, 21, 88, 29}, {65, 130, 3, 38, 73, 11, 108, 46, 81, 116, 89, 30}, {130, 4, 39, 74, 12, 109, 47, 82, 117, 55, 90, 31}, {32, 130, 99, 5, 40, 75, 13, 48, 83, 118, 56, 91}, {130, 100, 6, 41, 76, 14, 49, 84, 22, 119, 57, 92}, {66, 130, 101, 7, 42, 15, 50, 85, 23, 120, 58, 93}, {130, 67, 102, 8, 43, 110, 16, 51, 86, 24, 59, 94}, {33, 130, 68, 103, 9, 111, 17, 52, 87, 25, 60, 95}, {96, 34, 130, 69, 104, 10, 77, 112, 18, 53, 26, 61}, {0, 131, 38, 103, 76, 47, 112, 20, 85, 56, 29, 94}, {1, 66, 131, 39, 104, 48, 113, 21, 86, 57, 30, 95}, {96, 2, 67, 131, 40, 105, 11, 49, 114, 87, 58, 31}, {32, 97, 3, 68, 131, 41, 106, 12, 77, 50, 115, 59}, {98, 131, 4, 69, 42, 107, 13, 78, 51, 116, 22, 60}, {131, 5, 70, 43, 108, 14, 79, 52, 117, 23, 88, 61}, {33, 131, 6, 71, 109, 15, 80, 53, 118, 24, 89, 62}, {34, 99, 131, 7, 72, 16, 81, 54, 119, 25, 90, 63}, {64, 35, 100, 131, 8, 73, 44, 17, 82, 120, 26, 91}, {65, 131, 36, 101, 9, 74, 45, 110, 18, 83, 27, 92}, {131, 37, 102, 10, 75, 46, 111, 19, 84, 55, 28, 93}, {0, 132, 101, 71, 41, 111, 81, 51, 21, 91, 61, 31}, {32, 1, 132, 102, 72, 42, 11, 112, 82, 52, 92, 62}, {2, 132, 103, 73, 43, 12, 113, 83, 53, 22, 93, 63}, {64, 33, 3, 132, 104, 74, 13, 114, 84, 54, 23, 94}, {65, 34, 4, 132, 105, 75, 44, 14, 115, 85, 24, 95}, {96, 35, 132, 5, 106, 76, 45, 15, 116, 86, 55, 25}, {97, 66, 36, 132, 6, 107, 46, 16, 117, 87, 56, 26}, {98, 67, 132, 37, 7, 108, 77, 47, 17, 118, 57, 27}, {68, 132, 38, 8, 109, 78, 48, 18, 119, 88, 58, 28}, {99, 132, 69, 39, 9, 79, 49, 19, 120, 89, 59, 29}, {100, 132, 70, 40, 10, 110, 80, 50, 20, 90, 60, 30}, {128, 129, 130, 131, 132, 121, 122, 123, 124, 125, 126, 127}]
------------

itertools-create-cards.py

# https://github.com/plagtag/ProjectiveGeometry-Game/blob/master/create_cards.py
from itertools import *

def create_cards(order):
    # nice reading on projective planes:
    # http://www.mathpuzzle.com/MAA/47-Fano/mathgames_05_30_06.html
    # In a projective plane, there are no parallel lines.
    # A projective plane of order n has n**2 + n + 1 points and lines,
    # with n+1 points on each line, and n+1 lines on each point.
    for min_factor in range(2, 1 + int(order ** 0.5)):
        if order % min_factor == 0:
            break
    else:
        min_factor = order
    cards = []
    for i in range(order):
        cards.append(set([i * order + j for j in range(order)] + [order * order]))
    for i in range(min_factor):
        for j in range(order):
            cards.append(set([k * order + (j + i * k) % order
                              for k in range(order)] + [order * order + 1 + i]))

    cards.append(set([order * order + i for i in range(min_factor + 1)]))
    return cards, order * order + order + 1

for i in [2,3,5,7,11]:

    cards, total = create_cards(i)
    print("order:", i)
    print("count:", total)
    print(cards)
    print("------------")

sage_ProjectiveGeometryDesign-create_cards.py

# install sage from conda
# Note: takes a while to calculate the sage deps... like 15 mins
# https://doc.sagemath.org/html/en/installation/conda.html
from sage.all import GF, designs

for i in [2, 3, 4, 5, 7, 8, 9, 11, 13]:
  print("GF input of", i)
  # https://github.com/sagemath/sage/blob/6ea1fe936cc7600983bdd76aaa221f6c7105e9e1/src/sage/combinat/designs/block_design.py#L170
  cards = designs.ProjectiveGeometryDesign(2,1,GF(i),point_coordinates=0).blocks()
  print("card count:", len(cards))
  print(cards)
  print("---------")

sage_ProjectiveGeometryDesign-output.txt

GF input of 2
card count: 7
[[0, 1, 6], [0, 2, 4], [0, 3, 5], [1, 2, 5], [1, 3, 4], [2, 3, 6], [4, 5, 6]]
---------
GF input of 3
card count: 13
[[0, 1, 2, 12], [0, 3, 6, 9], [0, 4, 8, 10], [0, 5, 7, 11], [1, 3, 8, 11], [1, 4, 7, 9], [1, 5, 6, 10], [2, 3, 7, 10], [2, 4, 6, 11], [2, 5, 8, 9], [3, 4, 5, 12], [6, 7, 8, 12], [9, 10, 11, 12]]
---------
GF input of 4
card count: 21
[[0, 1, 2, 3, 20], [0, 4, 8, 12, 16], [0, 5, 10, 15, 19], [0, 6, 11, 13, 17], [0, 7, 9, 14, 18], [1, 4, 11, 14, 19], [1, 5, 9, 13, 16], [1, 6, 8, 15, 18], [1, 7, 10, 12, 17], [2, 4, 9, 15, 17], [2, 5, 11, 12, 18], [2, 6, 10, 14, 16], [2, 7, 8, 13, 19], [3, 4, 10, 13, 18], [3, 5, 8, 14, 17], [3, 6, 9, 12, 19], [3, 7, 11, 15, 16], [4, 5, 6, 7, 20], [8, 9, 10, 11, 20], [12, 13, 14, 15, 20], [16, 17, 18, 19, 20]]
---------
GF input of 5
card count: 31
[[0, 1, 2, 3, 4, 30], [0, 5, 10, 15, 20, 25], [0, 6, 12, 18, 24, 26], [0, 7, 14, 16, 23, 27], [0, 8, 11, 19, 22, 28], [0, 9, 13, 17, 21, 29], [1, 5, 14, 18, 22, 29], [1, 6, 11, 16, 21, 25], [1, 7, 13, 19, 20, 26], [1, 8, 10, 17, 24, 27], [1, 9, 12, 15, 23, 28], [2, 5, 13, 16, 24, 28], [2, 6, 10, 19, 23, 29], [2, 7, 12, 17, 22, 25], [2, 8, 14, 15, 21, 26], [2, 9, 11, 18, 20, 27], [3, 5, 12, 19, 21, 27], [3, 6, 14, 17, 20, 28], [3, 7, 11, 15, 24, 29], [3, 8, 13, 18, 23, 25], [3, 9, 10, 16, 22, 26], [4, 5, 11, 17, 23, 26], [4, 6, 13, 15, 22, 27], [4, 7, 10, 18, 21, 28], [4, 8, 12, 16, 20, 29], [4, 9, 14, 19, 24, 25], [5, 6, 7, 8, 9, 30], [10, 11, 12, 13, 14, 30], [15, 16, 17, 18, 19, 30], [20, 21, 22, 23, 24, 30], [25, 26, 27, 28, 29, 30]]
---------
GF input of 7
card count: 57
[[0, 1, 2, 3, 4, 5, 6, 56], [0, 7, 14, 21, 28, 35, 42, 49], [0, 8, 16, 24, 32, 40, 48, 50], [0, 9, 18, 27, 29, 38, 47, 51], [0, 10, 20, 23, 33, 36, 46, 52], [0, 11, 15, 26, 30, 41, 45, 53], [0, 12, 17, 22, 34, 39, 44, 54], [0, 13, 19, 25, 31, 37, 43, 55], [1, 7, 20, 26, 32, 38, 44, 55], [1, 8, 15, 22, 29, 36, 43, 49], [1, 9, 17, 25, 33, 41, 42, 50], [1, 10, 19, 21, 30, 39, 48, 51], [1, 11, 14, 24, 34, 37, 47, 52], [1, 12, 16, 27, 31, 35, 46, 53], [1, 13, 18, 23, 28, 40, 45, 54], [2, 7, 19, 24, 29, 41, 46, 54], [2, 8, 14, 27, 33, 39, 45, 55], [2, 9, 16, 23, 30, 37, 44, 49], [2, 10, 18, 26, 34, 35, 43, 50], [2, 11, 20, 22, 31, 40, 42, 51], [2, 12, 15, 25, 28, 38, 48, 52], [2, 13, 17, 21, 32, 36, 47, 53], [3, 7, 18, 22, 33, 37, 48, 53], [3, 8, 20, 25, 30, 35, 47, 54], [3, 9, 15, 21, 34, 40, 46, 55], [3, 10, 17, 24, 31, 38, 45, 49], [3, 11, 19, 27, 28, 36, 44, 50], [3, 12, 14, 23, 32, 41, 43, 51], [3, 13, 16, 26, 29, 39, 42, 52], [4, 7, 17, 27, 30, 40, 43, 52], [4, 8, 19, 23, 34, 38, 42, 53], [4, 9, 14, 26, 31, 36, 48, 54], [4, 10, 16, 22, 28, 41, 47, 55], [4, 11, 18, 25, 32, 39, 46, 49], [4, 12, 20, 21, 29, 37, 45, 50], [4, 13, 15, 24, 33, 35, 44, 51], [5, 7, 16, 25, 34, 36, 45, 51], [5, 8, 18, 21, 31, 41, 44, 52], [5, 9, 20, 24, 28, 39, 43, 53], [5, 10, 15, 27, 32, 37, 42, 54], [5, 11, 17, 23, 29, 35, 48, 55], [5, 12, 19, 26, 33, 40, 47, 49], [5, 13, 14, 22, 30, 38, 46, 50], [6, 7, 15, 23, 31, 39, 47, 50], [6, 8, 17, 26, 28, 37, 46, 51], [6, 9, 19, 22, 32, 35, 45, 52], [6, 10, 14, 25, 29, 40, 44, 53], [6, 11, 16, 21, 33, 38, 43, 54], [6, 12, 18, 24, 30, 36, 42, 55], [6, 13, 20, 27, 34, 41, 48, 49], [7, 8, 9, 10, 11, 12, 13, 56], [14, 15, 16, 17, 18, 19, 20, 56], [21, 22, 23, 24, 25, 26, 27, 56], [28, 29, 30, 31, 32, 33, 34, 56], [35, 36, 37, 38, 39, 40, 41, 56], [42, 43, 44, 45, 46, 47, 48, 56], [49, 50, 51, 52, 53, 54, 55, 56]]
---------
GF input of 8
card count: 73
[[0, 1, 2, 3, 4, 5, 6, 7, 72], [0, 8, 16, 24, 32, 40, 48, 56, 64], [0, 9, 18, 27, 36, 45, 54, 63, 71], [0, 10, 19, 28, 37, 46, 55, 57, 65], [0, 11, 20, 29, 38, 47, 49, 58, 66], [0, 12, 21, 30, 39, 41, 50, 59, 67], [0, 13, 22, 31, 33, 42, 51, 60, 68], [0, 14, 23, 25, 34, 43, 52, 61, 69], [0, 15, 17, 26, 35, 44, 53, 62, 70], [1, 8, 20, 31, 34, 46, 53, 59, 71], [1, 9, 17, 25, 33, 41, 49, 57, 64], [1, 10, 22, 29, 35, 40, 52, 63, 67], [1, 11, 16, 28, 39, 42, 54, 61, 70], [1, 12, 23, 26, 38, 45, 51, 56, 65], [1, 13, 19, 24, 36, 47, 50, 62, 69], [1, 14, 21, 27, 32, 44, 55, 58, 68], [1, 15, 18, 30, 37, 43, 48, 60, 66], [2, 8, 21, 25, 35, 47, 54, 60, 65], [2, 9, 19, 31, 38, 44, 48, 61, 67], [2, 10, 18, 26, 34, 42, 50, 58, 64], [2, 11, 23, 30, 36, 40, 53, 57, 68], [2, 12, 16, 29, 33, 43, 55, 62, 71], [2, 13, 17, 27, 39, 46, 52, 56, 66], [2, 14, 20, 24, 37, 41, 51, 63, 70], [2, 15, 22, 28, 32, 45, 49, 59, 69], [3, 8, 22, 26, 36, 41, 55, 61, 66], [3, 9, 23, 29, 32, 46, 50, 60, 70], [3, 10, 20, 25, 39, 45, 48, 62, 68], [3, 11, 19, 27, 35, 43, 51, 59, 64], [3, 12, 17, 31, 37, 40, 54, 58, 69], [3, 13, 16, 30, 34, 44, 49, 63, 65], [3, 14, 18, 28, 33, 47, 53, 56, 67], [3, 15, 21, 24, 38, 42, 52, 57, 71], [4, 8, 23, 27, 37, 42, 49, 62, 67], [4, 9, 22, 24, 39, 43, 53, 58, 65], [4, 10, 17, 30, 32, 47, 51, 61, 71], [4, 11, 21, 26, 33, 46, 48, 63, 69], [4, 12, 20, 28, 36, 44, 52, 60, 64], [4, 13, 18, 25, 38, 40, 55, 59, 70], [4, 14, 16, 31, 35, 45, 50, 57, 66], [4, 15, 19, 29, 34, 41, 54, 56, 68], [5, 8, 17, 28, 38, 43, 50, 63, 68], [5, 9, 20, 30, 35, 42, 55, 56, 69], [5, 10, 23, 24, 33, 44, 54, 59, 66], [5, 11, 18, 31, 32, 41, 52, 62, 65], [5, 12, 22, 27, 34, 47, 48, 57, 70], [5, 13, 21, 29, 37, 45, 53, 61, 64], [5, 14, 19, 26, 39, 40, 49, 60, 71], [5, 15, 16, 25, 36, 46, 51, 58, 67], [6, 8, 18, 29, 39, 44, 51, 57, 69], [6, 9, 16, 26, 37, 47, 52, 59, 68], [6, 10, 21, 31, 36, 43, 49, 56, 70], [6, 11, 17, 24, 34, 45, 55, 60, 67], [6, 12, 19, 25, 32, 42, 53, 63, 66], [6, 13, 23, 28, 35, 41, 48, 58, 71], [6, 14, 22, 30, 38, 46, 54, 62, 64], [6, 15, 20, 27, 33, 40, 50, 61, 65], [7, 8, 19, 30, 33, 45, 52, 58, 70], [7, 9, 21, 28, 34, 40, 51, 62, 66], [7, 10, 16, 27, 38, 41, 53, 60, 69], [7, 11, 22, 25, 37, 44, 50, 56, 71], [7, 12, 18, 24, 35, 46, 49, 61, 68], [7, 13, 20, 26, 32, 43, 54, 57, 67], [7, 14, 17, 29, 36, 42, 48, 59, 65], [7, 15, 23, 31, 39, 47, 55, 63, 64], [8, 9, 10, 11, 12, 13, 14, 15, 72], [16, 17, 18, 19, 20, 21, 22, 23, 72], [24, 25, 26, 27, 28, 29, 30, 31, 72], [32, 33, 34, 35, 36, 37, 38, 39, 72], [40, 41, 42, 43, 44, 45, 46, 47, 72], [48, 49, 50, 51, 52, 53, 54, 55, 72], [56, 57, 58, 59, 60, 61, 62, 63, 72], [64, 65, 66, 67, 68, 69, 70, 71, 72]]
---------
GF input of 9
card count: 91
[[0, 1, 2, 3, 4, 5, 6, 7, 8, 90], [0, 9, 18, 27, 36, 45, 54, 63, 72, 81], [0, 10, 20, 30, 40, 50, 60, 70, 80, 89], [0, 11, 21, 31, 41, 51, 61, 71, 73, 82], [0, 12, 22, 32, 42, 52, 62, 64, 74, 83], [0, 13, 23, 33, 43, 53, 55, 65, 75, 84], [0, 14, 24, 34, 44, 46, 56, 66, 76, 85], [0, 15, 25, 35, 37, 47, 57, 67, 77, 86], [0, 16, 26, 28, 38, 48, 58, 68, 78, 87], [0, 17, 19, 29, 39, 49, 59, 69, 79, 88], [1, 9, 22, 33, 38, 50, 57, 71, 79, 85], [1, 10, 19, 28, 37, 46, 55, 64, 73, 81], [1, 11, 23, 30, 44, 52, 54, 67, 78, 88], [1, 12, 26, 34, 36, 49, 60, 65, 77, 82], [1, 13, 24, 29, 41, 48, 62, 70, 72, 86], [1, 14, 21, 35, 43, 45, 58, 69, 74, 89], [1, 15, 20, 32, 39, 53, 61, 63, 76, 87], [1, 16, 18, 31, 42, 47, 59, 66, 80, 84], [1, 17, 25, 27, 40, 51, 56, 68, 75, 83], [2, 9, 23, 34, 39, 51, 58, 64, 80, 86], [2, 10, 26, 27, 41, 52, 57, 69, 76, 84], [2, 11, 20, 29, 38, 47, 56, 65, 74, 81], [2, 12, 24, 31, 37, 53, 54, 68, 79, 89], [2, 13, 19, 35, 36, 50, 61, 66, 78, 83], [2, 14, 25, 30, 42, 49, 55, 71, 72, 87], [2, 15, 22, 28, 44, 45, 59, 70, 75, 82], [2, 16, 21, 33, 40, 46, 62, 63, 77, 88], [2, 17, 18, 32, 43, 48, 60, 67, 73, 85], [3, 9, 24, 35, 40, 52, 59, 65, 73, 87], [3, 10, 18, 33, 44, 49, 61, 68, 74, 86], [3, 11, 19, 27, 42, 53, 58, 70, 77, 85], [3, 12, 21, 30, 39, 48, 57, 66, 75, 81], [3, 13, 25, 32, 38, 46, 54, 69, 80, 82], [3, 14, 20, 28, 36, 51, 62, 67, 79, 84], [3, 15, 26, 31, 43, 50, 56, 64, 72, 88], [3, 16, 23, 29, 37, 45, 60, 71, 76, 83], [3, 17, 22, 34, 41, 47, 55, 63, 78, 89], [4, 9, 25, 28, 41, 53, 60, 66, 74, 88], [4, 10, 23, 35, 42, 48, 56, 63, 79, 82], [4, 11, 18, 34, 37, 50, 62, 69, 75, 87], [4, 12, 20, 27, 43, 46, 59, 71, 78, 86], [4, 13, 22, 31, 40, 49, 58, 67, 76, 81], [4, 14, 26, 33, 39, 47, 54, 70, 73, 83], [4, 15, 21, 29, 36, 52, 55, 68, 80, 85], [4, 16, 19, 32, 44, 51, 57, 65, 72, 89], [4, 17, 24, 30, 38, 45, 61, 64, 77, 84], [5, 9, 26, 29, 42, 46, 61, 67, 75, 89], [5, 10, 25, 31, 39, 45, 62, 65, 78, 85], [5, 11, 24, 28, 43, 49, 57, 63, 80, 83], [5, 12, 18, 35, 38, 51, 55, 70, 76, 88], [5, 13, 21, 27, 44, 47, 60, 64, 79, 87], [5, 14, 23, 32, 41, 50, 59, 68, 77, 81], [5, 15, 19, 34, 40, 48, 54, 71, 74, 84], [5, 16, 22, 30, 36, 53, 56, 69, 73, 86], [5, 17, 20, 33, 37, 52, 58, 66, 72, 82], [6, 9, 19, 30, 43, 47, 62, 68, 76, 82], [6, 10, 21, 34, 38, 53, 59, 67, 72, 83], [6, 11, 26, 32, 40, 45, 55, 66, 79, 86], [6, 12, 25, 29, 44, 50, 58, 63, 73, 84], [6, 13, 18, 28, 39, 52, 56, 71, 77, 89], [6, 14, 22, 27, 37, 48, 61, 65, 80, 88], [6, 15, 24, 33, 42, 51, 60, 69, 78, 81], [6, 16, 20, 35, 41, 49, 54, 64, 75, 85], [6, 17, 23, 31, 36, 46, 57, 70, 74, 87], [7, 9, 20, 31, 44, 48, 55, 69, 77, 83], [7, 10, 24, 32, 36, 47, 58, 71, 75, 88], [7, 11, 22, 35, 39, 46, 60, 68, 72, 84], [7, 12, 19, 33, 41, 45, 56, 67, 80, 87], [7, 13, 26, 30, 37, 51, 59, 63, 74, 85], [7, 14, 18, 29, 40, 53, 57, 64, 78, 82], [7, 15, 23, 27, 38, 49, 62, 66, 73, 89], [7, 16, 25, 34, 43, 52, 61, 70, 79, 81], [7, 17, 21, 28, 42, 50, 54, 65, 76, 86], [8, 9, 21, 32, 37, 49, 56, 70, 78, 84], [8, 10, 22, 29, 43, 51, 54, 66, 77, 87], [8, 11, 25, 33, 36, 48, 59, 64, 76, 89], [8, 12, 23, 28, 40, 47, 61, 69, 72, 85], [8, 13, 20, 34, 42, 45, 57, 68, 73, 88], [8, 14, 19, 31, 38, 52, 60, 63, 75, 86], [8, 15, 18, 30, 41, 46, 58, 65, 79, 83], [8, 16, 24, 27, 39, 50, 55, 67, 74, 82], [8, 17, 26, 35, 44, 53, 62, 71, 80, 81], [9, 10, 11, 12, 13, 14, 15, 16, 17, 90], [18, 19, 20, 21, 22, 23, 24, 25, 26, 90], [27, 28, 29, 30, 31, 32, 33, 34, 35, 90], [36, 37, 38, 39, 40, 41, 42, 43, 44, 90], [45, 46, 47, 48, 49, 50, 51, 52, 53, 90], [54, 55, 56, 57, 58, 59, 60, 61, 62, 90], [63, 64, 65, 66, 67, 68, 69, 70, 71, 90], [72, 73, 74, 75, 76, 77, 78, 79, 80, 90], [81, 82, 83, 84, 85, 86, 87, 88, 89, 90]]
---------
GF input of 11
card count: 133
[[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 132], [0, 11, 22, 33, 44, 55, 66, 77, 88, 99, 110, 121], [0, 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 122], [0, 13, 26, 39, 52, 65, 67, 80, 93, 106, 119, 123], [0, 14, 28, 42, 45, 59, 73, 87, 90, 104, 118, 124], [0, 15, 30, 34, 49, 64, 68, 83, 98, 102, 117, 125], [0, 16, 32, 37, 53, 58, 74, 79, 95, 100, 116, 126], [0, 17, 23, 40, 46, 63, 69, 86, 92, 109, 115, 127], [0, 18, 25, 43, 50, 57, 75, 82, 89, 107, 114, 128], [0, 19, 27, 35, 54, 62, 70, 78, 97, 105, 113, 129], [0, 20, 29, 38, 47, 56, 76, 85, 94, 103, 112, 130], [0, 21, 31, 41, 51, 61, 71, 81, 91, 101, 111, 131], [1, 11, 32, 42, 52, 62, 72, 82, 92, 102, 112, 131], [1, 12, 23, 34, 45, 56, 67, 78, 89, 100, 111, 121], [1, 13, 25, 37, 49, 61, 73, 85, 97, 109, 110, 122], [1, 14, 27, 40, 53, 55, 68, 81, 94, 107, 120, 123], [1, 15, 29, 43, 46, 60, 74, 77, 91, 105, 119, 124], [1, 16, 31, 35, 50, 65, 69, 84, 88, 103, 118, 125], [1, 17, 22, 38, 54, 59, 75, 80, 96, 101, 117, 126], [1, 18, 24, 41, 47, 64, 70, 87, 93, 99, 116, 127], [1, 19, 26, 33, 51, 58, 76, 83, 90, 108, 115, 128], [1, 20, 28, 36, 44, 63, 71, 79, 98, 106, 114, 129], [1, 21, 30, 39, 48, 57, 66, 86, 95, 104, 113, 130], [2, 11, 31, 40, 49, 58, 67, 87, 96, 105, 114, 130], [2, 12, 22, 43, 53, 63, 73, 83, 93, 103, 113, 131], [2, 13, 24, 35, 46, 57, 68, 79, 90, 101, 112, 121], [2, 14, 26, 38, 50, 62, 74, 86, 98, 99, 111, 122], [2, 15, 28, 41, 54, 56, 69, 82, 95, 108, 110, 123], [2, 16, 30, 33, 47, 61, 75, 78, 92, 106, 120, 124], [2, 17, 32, 36, 51, 55, 70, 85, 89, 104, 119, 125], [2, 18, 23, 39, 44, 60, 76, 81, 97, 102, 118, 126], [2, 19, 25, 42, 48, 65, 71, 77, 94, 100, 117, 127], [2, 20, 27, 34, 52, 59, 66, 84, 91, 109, 116, 128], [2, 21, 29, 37, 45, 64, 72, 80, 88, 107, 115, 129], [3, 11, 30, 38, 46, 65, 73, 81, 89, 108, 116, 129], [3, 12, 32, 41, 50, 59, 68, 77, 97, 106, 115, 130], [3, 13, 23, 33, 54, 64, 74, 84, 94, 104, 114, 131], [3, 14, 25, 36, 47, 58, 69, 80, 91, 102, 113, 121], [3, 15, 27, 39, 51, 63, 75, 87, 88, 100, 112, 122], [3, 16, 29, 42, 44, 57, 70, 83, 96, 109, 111, 123], [3, 17, 31, 34, 48, 62, 76, 79, 93, 107, 110, 124], [3, 18, 22, 37, 52, 56, 71, 86, 90, 105, 120, 125], [3, 19, 24, 40, 45, 61, 66, 82, 98, 103, 119, 126], [3, 20, 26, 43, 49, 55, 72, 78, 95, 101, 118, 127], [3, 21, 28, 35, 53, 60, 67, 85, 92, 99, 117, 128], [4, 11, 29, 36, 54, 61, 68, 86, 93, 100, 118, 128], [4, 12, 31, 39, 47, 55, 74, 82, 90, 109, 117, 129], [4, 13, 22, 42, 51, 60, 69, 78, 98, 107, 116, 130], [4, 14, 24, 34, 44, 65, 75, 85, 95, 105, 115, 131], [4, 15, 26, 37, 48, 59, 70, 81, 92, 103, 114, 121], [4, 16, 28, 40, 52, 64, 76, 77, 89, 101, 113, 122], [4, 17, 30, 43, 45, 58, 71, 84, 97, 99, 112, 123], [4, 18, 32, 35, 49, 63, 66, 80, 94, 108, 111, 124], [4, 19, 23, 38, 53, 57, 72, 87, 91, 106, 110, 125], [4, 20, 25, 41, 46, 62, 67, 83, 88, 104, 120, 126], [4, 21, 27, 33, 50, 56, 73, 79, 96, 102, 119, 127], [5, 11, 28, 34, 51, 57, 74, 80, 97, 103, 120, 127], [5, 12, 30, 37, 44, 62, 69, 87, 94, 101, 119, 128], [5, 13, 32, 40, 48, 56, 75, 83, 91, 99, 118, 129], [5, 14, 23, 43, 52, 61, 70, 79, 88, 108, 117, 130], [5, 15, 25, 35, 45, 55, 76, 86, 96, 106, 116, 131], [5, 16, 27, 38, 49, 60, 71, 82, 93, 104, 115, 121], [5, 17, 29, 41, 53, 65, 66, 78, 90, 102, 114, 122], [5, 18, 31, 33, 46, 59, 72, 85, 98, 100, 113, 123], [5, 19, 22, 36, 50, 64, 67, 81, 95, 109, 112, 124], [5, 20, 24, 39, 54, 58, 73, 77, 92, 107, 111, 125], [5, 21, 26, 42, 47, 63, 68, 84, 89, 105, 110, 126], [6, 11, 27, 43, 48, 64, 69, 85, 90, 106, 111, 126], [6, 12, 29, 35, 52, 58, 75, 81, 98, 104, 110, 127], [6, 13, 31, 38, 45, 63, 70, 77, 95, 102, 120, 128], [6, 14, 22, 41, 49, 57, 76, 84, 92, 100, 119, 129], [6, 15, 24, 33, 53, 62, 71, 80, 89, 109, 118, 130], [6, 16, 26, 36, 46, 56, 66, 87, 97, 107, 117, 131], [6, 17, 28, 39, 50, 61, 72, 83, 94, 105, 116, 121], [6, 18, 30, 42, 54, 55, 67, 79, 91, 103, 115, 122], [6, 19, 32, 34, 47, 60, 73, 86, 88, 101, 114, 123], [6, 20, 23, 37, 51, 65, 68, 82, 96, 99, 113, 124], [6, 21, 25, 40, 44, 59, 74, 78, 93, 108, 112, 125], [7, 11, 26, 41, 45, 60, 75, 79, 94, 109, 113, 125], [7, 12, 28, 33, 49, 65, 70, 86, 91, 107, 112, 126], [7, 13, 30, 36, 53, 59, 76, 82, 88, 105, 111, 127], [7, 14, 32, 39, 46, 64, 71, 78, 96, 103, 110, 128], [7, 15, 23, 42, 50, 58, 66, 85, 93, 101, 120, 129], [7, 16, 25, 34, 54, 63, 72, 81, 90, 99, 119, 130], [7, 17, 27, 37, 47, 57, 67, 77, 98, 108, 118, 131], [7, 18, 29, 40, 51, 62, 73, 84, 95, 106, 117, 121], [7, 19, 31, 43, 44, 56, 68, 80, 92, 104, 116, 122], [7, 20, 22, 35, 48, 61, 74, 87, 89, 102, 115, 123], [7, 21, 24, 38, 52, 55, 69, 83, 97, 100, 114, 124], [8, 11, 25, 39, 53, 56, 70, 84, 98, 101, 115, 124], [8, 12, 27, 42, 46, 61, 76, 80, 95, 99, 114, 125], [8, 13, 29, 34, 50, 55, 71, 87, 92, 108, 113, 126], [8, 14, 31, 37, 54, 60, 66, 83, 89, 106, 112, 127], [8, 15, 22, 40, 47, 65, 72, 79, 97, 104, 111, 128], [8, 16, 24, 43, 51, 59, 67, 86, 94, 102, 110, 129], [8, 17, 26, 35, 44, 64, 73, 82, 91, 100, 120, 130], [8, 18, 28, 38, 48, 58, 68, 78, 88, 109, 119, 131], [8, 19, 30, 41, 52, 63, 74, 85, 96, 107, 118, 121], [8, 20, 32, 33, 45, 57, 69, 81, 93, 105, 117, 122], [8, 21, 23, 36, 49, 62, 75, 77, 90, 103, 116, 123], [9, 11, 24, 37, 50, 63, 76, 78, 91, 104, 117, 123], [9, 12, 26, 40, 54, 57, 71, 85, 88, 102, 116, 124], [9, 13, 28, 43, 47, 62, 66, 81, 96, 100, 115, 125], [9, 14, 30, 35, 51, 56, 72, 77, 93, 109, 114, 126], [9, 15, 32, 38, 44, 61, 67, 84, 90, 107, 113, 127], [9, 16, 23, 41, 48, 55, 73, 80, 98, 105, 112, 128], [9, 17, 25, 33, 52, 60, 68, 87, 95, 103, 111, 129], [9, 18, 27, 36, 45, 65, 74, 83, 92, 101, 110, 130], [9, 19, 29, 39, 49, 59, 69, 79, 89, 99, 120, 131], [9, 20, 31, 42, 53, 64, 75, 86, 97, 108, 119, 121], [9, 21, 22, 34, 46, 58, 70, 82, 94, 106, 118, 122], [10, 11, 23, 35, 47, 59, 71, 83, 95, 107, 119, 122], [10, 12, 25, 38, 51, 64, 66, 79, 92, 105, 118, 123], [10, 13, 27, 41, 44, 58, 72, 86, 89, 103, 117, 124], [10, 14, 29, 33, 48, 63, 67, 82, 97, 101, 116, 125], [10, 15, 31, 36, 52, 57, 73, 78, 94, 99, 115, 126], [10, 16, 22, 39, 45, 62, 68, 85, 91, 108, 114, 127], [10, 17, 24, 42, 49, 56, 74, 81, 88, 106, 113, 128], [10, 18, 26, 34, 53, 61, 69, 77, 96, 104, 112, 129], [10, 19, 28, 37, 46, 55, 75, 84, 93, 102, 111, 130], [10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 131], [10, 21, 32, 43, 54, 65, 76, 87, 98, 109, 120, 121], [11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 132], [22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 132], [33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 132], [44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 132], [55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 132], [66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 132], [77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 132], [88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 132], [99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 132], [110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 132], [121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132]]
---------
GF input of 13
card count: 183
[[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 182], [0, 13, 26, 39, 52, 65, 78, 91, 104, 117, 130, 143, 156, 169], [0, 14, 28, 42, 56, 70, 84, 98, 112, 126, 140, 154, 168, 170], [0, 15, 30, 45, 60, 75, 90, 92, 107, 122, 137, 152, 167, 171], [0, 16, 32, 48, 64, 67, 83, 99, 115, 118, 134, 150, 166, 172], [0, 17, 34, 51, 55, 72, 89, 93, 110, 127, 131, 148, 165, 173], [0, 18, 36, 41, 59, 77, 82, 100, 105, 123, 141, 146, 164, 174], [0, 19, 38, 44, 63, 69, 88, 94, 113, 119, 138, 144, 163, 175], [0, 20, 27, 47, 54, 74, 81, 101, 108, 128, 135, 155, 162, 176], [0, 21, 29, 50, 58, 66, 87, 95, 116, 124, 132, 153, 161, 177], [0, 22, 31, 40, 62, 71, 80, 102, 111, 120, 142, 151, 160, 178], [0, 23, 33, 43, 53, 76, 86, 96, 106, 129, 139, 149, 159, 179], [0, 24, 35, 46, 57, 68, 79, 103, 114, 125, 136, 147, 158, 180], [0, 25, 37, 49, 61, 73, 85, 97, 109, 121, 133, 145, 157, 181], [1, 13, 38, 50, 62, 74, 86, 98, 110, 122, 134, 146, 158, 181], [1, 14, 27, 40, 53, 66, 79, 92, 105, 118, 131, 144, 157, 169], 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