幸运26是一个著名的数学游戏.自1986年美国数学竞赛中,得出144种解答后,迄今为止,能否得出第145个仍然是个未知数.幸运26 数字的填补方式是从最顶部那个开始,向右依次填写. 规则 将标有数字1~12的棋子放在棋盘上圆孔内,使棋盘上任意一条直线上数字之和为26. 1, 7, 2, 1, 9, 8,10, 6, 5, 3, 4,11,12 2, 3, 2, 8,10,11, 1, 7, 9, 5, 6, 4,12 3, 7, 1, 9, 8,10, 3, 6,11, 2, 5, 4,12 4, 1, 7, 3, 8,10, 9, 6, 5, 2,11, 4,12 5, 6, 4, 8, 7, 9, 1,10,11, 5, 3, 2,12 6, 3, 4, 8,10, 9, 1, 7,11, 5, 6, 2,12 7, 1, 9, 3,11, 5, 4, 8,10, 7, 6, 2,12 8, 1, 8, 4, 6,11, 7, 9, 5, 3,10, 2,12 9, 8, 7, 3, 2, 9,10,11, 6, 1, 5, 4,12 10, 6, 8, 2, 3, 9,11,10, 5, 1, 7, 4,12 11, 8, 1, 3,11, 6, 7, 5, 9, 4, 2,10,12 12, 9, 1, 7, 5,11, 4,10, 8, 3, 2, 6,12 13, 4, 5, 3,10, 7, 2,11, 8, 9, 1, 6,12 14, 3, 5, 1,11, 7, 4,10, 6, 9, 2, 8,12 15, 5, 9, 1,10, 2, 7, 8,11, 6, 3, 4,12 16, 8, 3, 7, 6, 9, 2,11,10, 5, 1, 4,12 17, 4, 1, 5,10,11, 2, 9, 6, 7, 3, 8,12 18, 5, 1, 3,11, 9, 4, 8, 6, 7, 2,10,12 19, 12, 7, 8, 3, 4, 6, 9, 5,11, 2,10, 1 20, 7,11, 4, 5, 3, 9, 8, 2,12, 6,10, 1 21, 12, 4,11, 7, 3, 6, 2, 9, 8, 5,10, 1 22, 12, 9, 6, 2, 3,11, 7, 4, 8, 5,10, 1 23, 5,11, 4, 7, 3, 9, 6, 2,12, 8,10, 1 24, 10, 9, 5, 3, 4,12, 6, 2, 8, 7,11, 1 25, 7, 9, 5, 6, 4,12, 3, 2, 8,10,11, 1 26, 7,12,11, 4, 3, 6, 5, 9, 8,10, 2, 1 27, 10, 2,12, 5, 9, 6, 3, 4, 7, 8,11, 1 28, 12, 4,10, 2, 8, 9, 5, 3, 6, 7,11, 1 29, 2,10, 7, 9, 5, 6, 4, 3,12,11, 8, 1 30, 3,11, 6, 7, 5, 9, 4, 2,10,12, 8, 1 31, 6, 5,12, 4,11, 3, 7, 2,10, 9, 8, 1 32, 8, 9,10, 2, 7, 3,11, 4,12, 5, 6, 1 33, 9, 8,11, 2, 7,10, 3, 5, 4,12, 6, 1 34, 12, 6,11, 3, 5,10, 2, 7, 4, 9, 8, 1 35, 11, 5,12, 3, 7, 9, 2, 6, 4,10, 8, 1 36, 9,10, 7, 2, 5, 6,11, 3,12, 4, 8, 1 37, 7, 6, 8, 4, 9,11, 3, 1, 5,12,10, 2 38, 4, 9, 5, 7, 6,11, 3, 1, 8,12,10, 2 39, 7, 3,11, 4,12, 5, 6, 1, 8, 9,10, 2 40, 7,12,11, 4, 3, 5, 6,10, 8, 9, 1, 2 41, 8,11,12, 3, 4, 5, 6,10, 7, 9, 1, 2 42, 11, 5, 9, 6, 4, 3, 8, 7,12, 1,10, 2 43, 6, 5, 9,12, 3, 4, 1, 8,11, 7,10, 2 44, 5,11, 3, 6, 4, 9, 8, 1,12, 7,10, 2 45, 8, 9, 5, 3, 6, 7,11, 1,12, 4,10, 2 46, 12, 3,11, 5, 6, 9, 1, 7, 4, 8,10, 2 47, 9, 6, 7, 3, 8,12, 4, 1, 5,10,11, 2 48, 7,10, 3, 8, 1, 9, 6, 4,12, 5,11, 2 49, 10, 1,12, 7, 8, 3, 4, 6, 9, 5,11, 2 50, 12, 6,10, 7, 1, 5, 4,11, 9, 3, 8, 2 51, 3, 8,10, 4,11, 5, 7, 1, 9,12, 6, 2 52, 7, 4,12,10, 5, 1, 3, 9,11, 6, 8, 2 53, 3,12, 4, 6, 5, 9, 7, 1,11,10, 8, 2 54, 12, 5, 9, 6, 3, 4, 7, 8,11, 1,10, 2 55, 10, 4,12, 1,11, 7, 6, 3, 5, 9, 8, 2 56, 6,12, 4, 3, 5, 9,10, 1,11, 7, 8, 2 57, 1, 9, 7,10, 6, 5, 4, 3,12,11, 8, 2 58, 9, 6, 7,10, 1, 5, 4, 8,12, 3,11, 2 59, 12, 8, 4, 5, 1,10, 7, 6, 9, 2,11, 3 60, 5, 4, 8, 7,10, 9, 2, 1, 6,12,11, 3 61, 5,10, 2, 7, 4, 9, 8, 1,12, 6,11, 3 62, 6,11, 8, 7, 2,10, 1, 9, 5,12, 4, 3 63, 2, 7,12, 8, 9, 1, 5, 6,10,11, 4, 3 64, 8,10,12, 2, 6, 7, 5, 9, 4,11, 1, 3 65, 8, 7,12, 2, 9, 1,11, 6,10, 5, 4, 3 66, 6,11, 2, 8, 1, 9, 7, 4,12, 5,10, 3 67, 9,11, 4, 5, 1, 7,10, 6,12, 2, 8, 3 68, 10, 8, 9, 1, 7,12, 4, 5, 2,11, 6, 3 69, 10, 5,12, 4, 7, 9, 1, 8, 2,11, 6, 3 70, 4,12, 5, 9, 1,10, 2, 7, 8,11, 6, 3 71, 1, 9, 6,11, 5, 7, 2, 4,10,12, 8, 3 72, 2,11, 4, 7, 6,10, 5, 1, 9,12, 8, 3 73, 11, 9, 6, 1, 5, 7,12, 4,10, 2, 8, 3 74, 8, 7,12, 1,10, 2,11, 5, 9, 6, 4, 3 75, 12,11, 8, 1, 2,10, 7, 9, 5, 6, 4, 3 76, 4, 6, 9, 5,11, 2,10, 1,12, 7, 8, 3 77, 7, 6, 9, 2,11,10, 5, 1, 4,12, 8, 3 78, 1,11, 4, 9, 5, 7, 6, 2,12,10, 8, 3 79, 12, 7, 5, 1, 6, 9,11, 3, 8, 2,10, 4 80, 12, 1,11, 7, 6, 3, 5, 9, 8, 2,10, 4 81, 2, 7, 5,11, 6, 9, 1, 3, 8,12,10, 4 82, 7, 8,11, 2, 9, 1,12, 6,10, 5, 3, 4 83, 11,12, 7, 1, 2,10, 8, 9, 5, 6, 3, 4 84, 3,12, 9, 5, 6, 2,10, 7,11, 8, 1, 4 85, 2,10,11, 5, 9, 3, 7, 6, 8,12, 1, 4 86, 11,12, 7, 2, 1, 9, 8,10, 6, 5, 3, 4 87, 8, 6, 7, 2,10,12, 5, 1, 3,11, 9, 4 88, 12,10, 5, 1, 3, 9,11, 6, 8, 2, 7, 4 89, 3, 5,10, 6,12, 1, 9, 2,11, 8, 7, 4 90, 3, 6, 9, 5,12, 2,10, 1,11, 8, 7, 4 91, 10, 6, 9, 2, 8,12, 3, 5, 1,11, 7, 4 92, 1,12, 3, 8, 5, 9, 6, 2,10,11, 7, 4 93, 12, 6, 9, 5, 3,11, 1,10, 2, 8, 7, 4 94, 12, 5,10, 3, 6,11, 2, 8, 1, 9, 7, 4 95, 8, 6, 7,11, 1, 3, 5,10,12, 2, 9, 4 96, 1,10, 7, 6, 9, 2,11, 3,12, 8, 4, 5 97, 1, 6,11,10, 9, 2, 3, 7, 8,12, 4, 5 98, 12, 4, 7, 9, 1, 8, 2,11, 6, 3,10, 5 99, 4,12, 8, 7, 3, 2, 9,10,11, 6, 1, 5 100, 7, 9,11, 4, 6, 8, 3,10, 2,12, 1, 5 101, 8, 9, 2, 6, 3, 7,11, 4,12, 1,10, 5 102, 3, 9, 2, 8, 6,12, 4, 1, 7,11,10, 5 103, 10, 1,12, 9, 6, 2, 3,11, 7, 4, 8, 5 104, 4, 3, 8, 7,12, 2, 9, 1,11, 6,10, 5 105, 9, 5,11, 2,10, 1,12, 7, 8, 3, 4, 6 106, 3,11, 5, 2,10, 7,12, 1, 8, 9, 4, 6 107, 2, 9, 7, 3,12, 5,11, 1, 8,10, 4, 6 108, 5, 9, 7,10, 2, 1, 8,11,12, 3, 4, 6 109, 5, 1, 9, 8,12, 7, 2, 3, 4,11,10, 6 110, 7,11, 1, 3, 5,10,12, 2, 9, 4, 8, 6 111, 7, 3, 9, 5,11,10, 2, 4, 1,12, 8, 6 112, 1, 9, 3,11, 5,10, 2, 4, 7,12, 8, 6 113, 7, 2,10,12, 5, 1, 3,11, 9, 4, 8, 6 114, 1,11, 4,12, 2, 7, 3, 8, 9,10, 5, 6 115, 12, 2, 8, 3, 9,11, 4, 5, 1, 7,10, 6 116, 9, 4, 5,12, 1, 6, 3,11, 8, 2,10, 7 117, 1, 5, 4,11, 9, 3, 8, 2,12, 6,10, 7 118, 8,12, 4, 5, 1, 6,11,10, 9, 2, 3, 7 119, 4,11, 5, 1,10, 8,12, 2, 6, 9, 3, 7 120, 10, 6,12, 2, 8, 3, 9,11, 4, 5, 1, 7 121, 1,12, 4,11, 2, 5, 6, 9,10, 8, 3, 7 122, 1, 9, 6, 5,11, 3,12, 2,10, 8, 4, 7 123, 11, 1,10, 9, 5, 3, 4,12, 6, 2, 8, 7 124, 12, 1,10, 2,11, 5, 9, 6, 4, 3, 8, 7 125, 12, 2, 9, 1,11, 6,10, 5, 4, 3, 8, 7 126, 2, 4,10,12, 8, 3, 1, 9, 6,11, 5, 7 127, 2,12, 4,11, 1, 6, 5,10, 9, 8, 3, 7 128, 9, 1,10,11, 5, 3, 2,12, 6, 4, 8, 7 129, 3, 2, 9,10,11, 6, 1, 5, 4,12, 8, 7 130, 10, 9, 2, 1, 6,12,11, 3, 5, 4, 8, 7 131, 7,11, 3, 6, 2, 5,12, 9,10, 1, 4, 8 132, 2,11, 3,12, 1, 6, 5,10, 9, 7, 4, 8 133, 9, 2, 6,12, 3, 7, 1,11, 5, 4,10, 8 134, 3, 2, 6,12, 9, 1, 7, 5,11, 4,10, 8 135, 2,11, 6, 3,10, 5,12, 4, 7, 9, 1, 8 136, 4, 6,11, 7, 9, 5, 3,10, 2,12, 1, 8 137, 7,12, 5, 4, 3,11, 6,10, 2, 9, 1, 8 138, 3,10, 7, 2,11, 5,12, 4, 6, 9, 1, 8 139, 7, 3, 5, 4,12,11, 6, 1, 2, 9,10, 8 140, 3, 7, 1,12, 4,11, 2, 5, 6, 9,10, 8 141, 4, 7, 1, 9, 6, 5,11, 3,12, 2,10, 8 142, 4,10, 1, 9, 3, 5,11, 6,12, 2, 7, 8 143, 10, 9, 2, 1, 6,11,12, 4, 5, 3, 7, 8 144, 11, 2, 9, 1,12, 6,10, 5, 3, 4, 7, 8 145, 11, 1,10, 2,12, 5, 9, 6, 3, 4, 7, 8 146, 4, 1,10, 9,12, 5, 2, 6, 3,11, 7, 8 147, 2,10, 1,11, 3, 5, 9, 6,12, 4, 7, 8 148, 1, 9, 2,10, 6,11, 3, 4, 5,12, 7, 8 149, 12, 6, 9, 1, 7, 5,11,10, 4, 2, 3, 8 150, 2, 6, 9,11, 7, 5, 1,10, 4,12, 3, 8 151, 8,10, 6, 5, 3, 4,11,12, 7, 2, 1, 9 152, 2,10, 6,11, 3, 4, 5,12, 7, 8, 1, 9 153, 7, 4,12, 5,10, 3, 6,11, 2, 8, 1, 9 154, 3,11, 5,10, 2, 4, 7,12, 8, 6, 1, 9 155, 3,11, 5, 4, 8,10, 7, 6, 2,12, 1, 9 156, 5, 7, 6,11, 3, 1, 8,12,10, 2, 4, 9 157, 5, 7, 6, 2,12,10, 8, 3, 1,11, 4, 9 158, 6, 5, 2,12, 3,11, 1, 8, 4, 7,10, 9 159, 12, 5, 2, 6, 3,11, 7, 8, 4, 1,10, 9 160, 1, 8, 2,11, 6, 3,10, 5,12, 4, 7, 9 161, 2, 8, 4,10, 6, 1,11, 7,12, 3, 5, 9 162, 4, 2,10,12, 8, 1, 3,11, 6, 7, 5, 9 163, 5, 6, 4,12, 3, 2, 8,10,11, 1, 7, 9 164, 2, 1, 6,12,11, 3, 5, 4, 8, 7,10, 9 165, 6, 5, 2,11, 4,12, 1, 7, 3, 8,10, 9 166, 5, 3, 4,12, 6, 2, 8, 7,11, 1,10, 9 167, 2, 1, 6,11,12, 4, 5, 3, 7, 8,10, 9 168, 6, 4,12, 5,11, 2, 7,10, 3, 8, 1, 9 169, 6,11, 5, 7, 2, 4,10,12, 8, 3, 1, 9 170, 8, 1, 6, 5,12, 4,11, 3, 7, 2,10, 9 171, 2, 4, 6, 8,12, 1,11, 3,10, 5, 7, 9 172, 2, 8, 6,12, 4, 1, 7,11,10, 5, 3, 9 173, 8, 2,12, 6,10, 1, 7,11, 4, 5, 3, 9 174, 7, 4, 1,12, 3, 8, 5, 9, 6, 2,10,11 175, 6, 7, 5, 9, 4, 2,10,12, 8, 1, 3,11 176, 4, 9, 5, 7, 6, 2,12,10, 8, 3, 1,11 177, 4,12, 2, 7, 3, 8, 9,10, 5, 6, 1,11 178, 8, 2,10, 7, 9, 4, 5,12, 1, 6, 3,11 179, 5, 2,10, 7,12, 1, 8, 9, 4, 6, 3,11 180, 7, 1,10, 6,12, 2, 8, 9, 3, 5, 4,11 181, 1, 3, 8,10,12, 2, 6, 7, 5, 9, 4,11 182, 12, 3, 4, 6, 5, 9, 7,10, 2, 1, 8,11 183, 12, 3, 4, 5, 6,10, 7, 9, 1, 2, 8,11 184, 2, 8, 1, 9, 7, 4,12, 5,10, 3, 6,11 185, 12, 4, 5, 3, 7, 8,10, 9, 2, 1, 6,11 186, 1, 7, 2, 8,10, 4,12, 3, 9, 5, 6,11 187, 7, 4, 8, 5,10, 1,12, 9, 6, 2, 3,11 188, 6,10, 2, 9, 1, 8, 7,12, 5, 4, 3,11 189, 2, 5, 6, 9,10, 8, 3, 7, 1,12, 4,11 190, 2,10, 1, 5, 9, 8,12, 3, 6, 7, 4,11 以上列举了190种解答.其中许多是重复的.有些是镜向的,不能算作两种.只有70种不同答案.详述如下: 原答案第1,86,151号是相同的,且与40号是镜向的.记为1,86,151和40;(下同)4,165和121,140,189;57和41,183;127和114,177;78,157,176和64,181;71,126,169和81;95,110;8,136;69,98,135,160和66,94,153,184;43和84;138和48,168;15,70和62;116,178;92,174;111和85;14和91;67,115,120和50,117;46和122,141;112,154;7,155;93和147;97,118和9,99,129;59,96和58;148,152和137,188;83和26;29,75和108,182;139和143,167,185;60,130,164;35和107;63和109;34,61;5,128;102,172;146,159和131;101和21;3和68;18,87,113和37;30,162,175和11,38,156;52,88;12,51和134;22,103,187;180和20,173;119和23;44和106,179;89和82,144;90和27,54,145;16,77和17,47;56和24,123,166;65,104,125;19,49,76,105和42,74,124;33和13;53和2,25,163;73和79;28,45和55,80;31,170和32,39.上述只能算55种,其余15种没有重复.因此总共只有70种. 现用按一定顺序的穷举法,得出80种不同答案.现列举如下: 1, 1,9,8,10,6,5,3,4,11,12,7,2 2, 1,9,7,10,6,5,4,3,12,11,8,2 3, 1,6,5,10,9,6,3,7,2,12,4,11 4, 1,6,5,10,9,7,4,8,2,11,3,12 5, 1,10,9,8,7,3,6,4,12,11,5,2 6, 1,10,9,7,8,4,6,3,11,12,5,2 7, 1,8,4,7,10,9,6,5,2,12,3,11 8, 1,7,3,8,10,9,6,5,2,11,4,12 9, 1,9,6,11,5,7,2,4,10,12,8,3 10,1,11,4,9,5,7,6,2,12,10,8,3 11,1,5,7,11,9,6,2,8,3,12,4,10 12,1,5,7,9,11,4,6,8,3,10,2,12 13,1,11,7,6,8,4,9,2,12,10,5,3 14,1,8,4,6,11,7,9,5,3,10,2,12 15,1,8,2,11,6,3,10,5,12,4,7,9 16,1,6,3,11,8,2,10,7,9,4,5,12 17,1,8,11,7,10,2,6,5,9,12,3,4 18,1,8,3,10,7,2,11,5,12,4,6,9 19,1,10,2,7,8,11,6,3,4,12,5,9 20,1,7,2,10,8,3,11,6,9,4,5,12 21,1,12,3,8,5,9,6,2,10,11,7,4 22,1,5,9,8,12,3,6,7,4,11,2,10 23,1,8,2,12,5,3,9,7,11,4,6,10 24,1,5,3,12,8,2,9,6,10,4,7,11 25,1,12,8,6,7,3,9,5,11,10,2,4 26,1,6,2,12,7,3,9,5,11,4,8,10 27,1,7,3,12,6,2,9,8,10,4,5,11 28,1,7,3,6,12,8,9,2,4,10,5,11 29,1,6,11,10,9,2,3,7,8,12,4,5 30,1,10,7,6,9,2,11,3,12,8,4,5 31,1,9,2,10,6,11,3,4,5,12,7,8 32,1,9,2,6,10,7,11,4,5,8,3,12 33,1,7,10,6,12,2,8,3,9,11,4,5 34,1,7,4,12,6,8,2,3,9,11,10,5 35,1,6,8,12,7,4,2,10,5,11,3,9 36,1,12,2,6,7,10,8,4,5,11,3,9 37,1,7,4,8,10,2,12,3,11,5,6,9 38,1,10,4,8,7,2,12,6,11,5,3,9 39,1,7,2,8,10,4,12,3,9,5,6,11 40,1,10,2,8,7,4,12,6,9,5,3,11 41,2,10,8,9,5,6,3,4,11,12,7,1 42,2,10,7,9,5,6,4,3,12,11,8,1 43,2,9,10,8,7,3,5,4,12,11,6,1 44,2,9,10,7,8,4,5,3,11,12,6,1 45,2,11,4,7,6,10,5,1,9,12,8,3 46,2,8,4,10,6,7,5,1,12,9,11,3 47,2,6,4,10,8,1,11,5,12,3,7,9 48,2,8,4,10,6,1,11,7,12,3,5,9 49,2,12,6,4,8,7,9,1,10,11,5,3 50,2,5,4,12,7,1,9,8,10,3,6,11 51,2,7,12,8,9,1,5,6,10,11,4,3 52,2,7,4,9,8,1,12,6,11,3,5,10 53,2,9,7,5,10,3,11,1,12,8,6,4 54,2,9,3,5,10,11,7,1,4,12,6,8 55,2,6,5,11,7,1,9,10,8,4,3,12 56,2,6,4,8,10,3,11,1,12,5,9,7 57,2,6,3,11,7,8,4,1,10,9,12,5 58,2,6,3,7,11,4,12,1,10,5,8,9 59,3,11,9,4,8,6,7,2,10,12,5,1 60,3,11,6,7,5,9,4,2,10,12,8,1 61,3,9,11,6,8,2,7,4,12,10,5,1 62,3,8,10,4,11,5,7,1,9,12,6,2 63,3,11,7,4,8,5,10,1,12,9,6,2 64,3,5,4,11,7,1,10,6,12,2,8,9 65,3,7,4,11,5,1,10,8,12,2,6,9 66,3,12,4,6,5,9,7,1,11,10,8,2 67,3,5,4,12,6,1,9,8,11,2,7,10 68,3,8,12,6,9,1,7,5,11,10,4,2 69,3,6,4,9,8,1,12,7,10,2,5,11 70,3,5,10,6,12,1,9,2,11,8,7,4 71,3,6,9,5,12,2,10,1,11,8,7,4 72,4,12,8,3,7,6,9,2,11,10,5,1 73,4,3,5,9,10,1,11,7,8,2,6,12 74,4,7,11,5,10,1,9,3,12,8,6,2 75,4,5,10,6,11,1,9,2,12,7,8,3 76,4,6,9,5,11,2,10,1,12,7,8,3 77,5,7,12,4,10,2,8,3,11,9,6,1 78,5,6,11,3,12,4,8,1,9,10,7,2 79,5,3,6,7,11,1,12,4,10,2,8,9 80,6,5,12,4,11,3,7,2,10,9,8,1 所谓镜向就是从一个端点向右和向左排列的两个答案.如:6,5,12,4,11,3,7,2,10,9,8,1和6,1,8,9,10,2,7,3,11,4,12,5 .