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.数字的填补方式是从最顶部那个开始,向右依次填写.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, 4,11,122, 3, 2, 8,10,11, 1, 7, 9, 5, 6, 4,123, 7, 1, 9, 8,10, 3, 6,11, 2, 5, 4,124, 1, 7, 3, 8,10, 9, 6, 5, 2,11, 4,125, 6, 4, 8, 7, 9, 1,10,11, 5, 3, 2,126, 3, 4, 8,10, 9, 1, 7,11, 5, 6, 2,127, 1, 9, 3,11, 5, 4, 8,10, 7, 6, 2,128, 1, 8, 4, 6,11, 7, 9, 5, 3,10, 2,129, 8, 7, 3, 2, 9,10,11, 6, 1, 5, 4,1210, 6, 8, 2, 3, 9,11,10, 5, 1, 7, 4,1211, 8, 1, 3,11, 6, 7, 5, 9, 4, 2,10,1212, 9, 1, 7, 5,11, 4,10, 8, 3, 2, 6,1213, 4, 5, 3,10, 7, 2,11, 8, 9, 1, 6,1214, 3, 5, 1,11, 7, 4,10, 6, 9, 2, 8,1215, 5, 9, 1,10, 2, 7, 8,11, 6, 3, 4,1216, 8, 3, 7, 6, 9, 2,11,10, 5, 1, 4,1217, 4, 1, 5,10,11, 2, 9, 6, 7, 3, 8,1218, 5, 1, 3,11, 9, 4, 8, 6, 7, 2,10,1219, 12, 7, 8, 3, 4, 6, 9, 5,11, 2,10, 120, 7,11, 4, 5, 3, 9, 8, 2,12, 6,10, 121, 12, 4,11, 7, 3, 6, 2, 9, 8, 5,10, 122, 12, 9, 6, 2, 3,11, 7, 4, 8, 5,10, 123, 5,11, 4, 7, 3, 9, 6, 2,12, 8,10, 124, 10, 9, 5, 3, 4,12, 6, 2, 8, 7,11, 125, 7, 9, 5, 6, 4,12, 3, 2, 8,10,11, 126, 7,12,11, 4, 3, 6, 5, 9, 8,10, 2, 127, 10, 2,12, 5, 9, 6, 3, 4, 7, 8,11, 128, 12, 4,10, 2, 8, 9, 5, 3, 6, 7,11, 129, 2,10, 7, 9, 5, 6, 4, 3,12,11, 8, 130, 3,11, 6, 7, 5, 9, 4, 2,10,12, 8, 131, 6, 5,12, 4,11, 3, 7, 2,10, 9, 8, 132, 8, 9,10, 2, 7, 3,11, 4,12, 5, 6, 133, 9, 8,11, 2, 7,10, 3, 5, 4,12, 6, 134, 12, 6,11, 3, 5,10, 2, 7, 4, 9, 8, 135, 11, 5,12, 3, 7, 9, 2, 6, 4,10, 8, 136, 9,10, 7, 2, 5, 6,11, 3,12, 4, 8, 137, 7, 6, 8, 4, 9,11, 3, 1, 5,12,10, 238, 4, 9, 5, 7, 6,11, 3, 1, 8,12,10, 239, 7, 3,11, 4,12, 5, 6, 1, 8, 9,10, 240, 7,12,11, 4, 3, 5, 6,10, 8, 9, 1, 241, 8,11,12, 3, 4, 5, 6,10, 7, 9, 1, 242, 11, 5, 9, 6, 4, 3, 8, 7,12, 1,10, 243, 6, 5, 9,12, 3, 4, 1, 8,11, 7,10, 244, 5,11, 3, 6, 4, 9, 8, 1,12, 7,10, 245, 8, 9, 5, 3, 6, 7,11, 1,12, 4,10, 246, 12, 3,11, 5, 6, 9, 1, 7, 4, 8,10, 247, 9, 6, 7, 3, 8,12, 4, 1, 5,10,11, 248, 7,10, 3, 8, 1, 9, 6, 4,12, 5,11, 249, 10, 1,12, 7, 8, 3, 4, 6, 9, 5,11, 250, 12, 6,10, 7, 1, 5, 4,11, 9, 3, 8, 251, 3, 8,10, 4,11, 5, 7, 1, 9,12, 6, 252, 7, 4,12,10, 5, 1, 3, 9,11, 6, 8, 253, 3,12, 4, 6, 5, 9, 7, 1,11,10, 8, 254, 12, 5, 9, 6, 3, 4, 7, 8,11, 1,10, 255, 10, 4,12, 1,11, 7, 6, 3, 5, 9, 8, 256, 6,12, 4, 3, 5, 9,10, 1,11, 7, 8, 257, 1, 9, 7,10, 6, 5, 4, 3,12,11, 8, 258, 9, 6, 7,10, 1, 5, 4, 8,12, 3,11, 259, 12, 8, 4, 5, 1,10, 7, 6, 9, 2,11, 360, 5, 4, 8, 7,10, 9, 2, 1, 6,12,11, 361, 5,10, 2, 7, 4, 9, 8, 1,12, 6,11, 362, 6,11, 8, 7, 2,10, 1, 9, 5,12, 4, 363, 2, 7,12, 8, 9, 1, 5, 6,10,11, 4, 364, 8,10,12, 2, 6, 7, 5, 9, 4,11, 1, 365, 8, 7,12, 2, 9, 1,11, 6,10, 5, 4, 366, 6,11, 2, 8, 1, 9, 7, 4,12, 5,10, 367, 9,11, 4, 5, 1, 7,10, 6,12, 2, 8, 368, 10, 8, 9, 1, 7,12, 4, 5, 2,11, 6, 369, 10, 5,12, 4, 7, 9, 1, 8, 2,11, 6, 370, 4,12, 5, 9, 1,10, 2, 7, 8,11, 6, 371, 1, 9, 6,11, 5, 7, 2, 4,10,12, 8, 372, 2,11, 4, 7, 6,10, 5, 1, 9,12, 8, 373, 11, 9, 6, 1, 5, 7,12, 4,10, 2, 8, 374, 8, 7,12, 1,10, 2,11, 5, 9, 6, 4, 375, 12,11, 8, 1, 2,10, 7, 9, 5, 6, 4, 376, 4, 6, 9, 5,11, 2,10, 1,12, 7, 8, 377, 7, 6, 9, 2,11,10, 5, 1, 4,12, 8, 378, 1,11, 4, 9, 5, 7, 6, 2,12,10, 8, 379, 12, 7, 5, 1, 6, 9,11, 3, 8, 2,10, 480, 12, 1,11, 7, 6, 3, 5, 9, 8, 2,10, 481, 2, 7, 5,11, 6, 9, 1, 3, 8,12,10, 482, 7, 8,11, 2, 9, 1,12, 6,10, 5, 3, 483, 11,12, 7, 1, 2,10, 8, 9, 5, 6, 3, 484, 3,12, 9, 5, 6, 2,10, 7,11, 8, 1, 485, 2,10,11, 5, 9, 3, 7, 6, 8,12, 1, 486, 11,12, 7, 2, 1, 9, 8,10, 6, 5, 3, 487, 8, 6, 7, 2,10,12, 5, 1, 3,11, 9, 488, 12,10, 5, 1, 3, 9,11, 6, 8, 2, 7, 489, 3, 5,10, 6,12, 1, 9, 2,11, 8, 7, 490, 3, 6, 9, 5,12, 2,10, 1,11, 8, 7, 491, 10, 6, 9, 2, 8,12, 3, 5, 1,11, 7, 492, 1,12, 3, 8, 5, 9, 6, 2,10,11, 7, 493, 12, 6, 9, 5, 3,11, 1,10, 2, 8, 7, 494, 12, 5,10, 3, 6,11, 2, 8, 1, 9, 7, 495, 8, 6, 7,11, 1, 3, 5,10,12, 2, 9, 496, 1,10, 7, 6, 9, 2,11, 3,12, 8, 4, 597, 1, 6,11,10, 9, 2, 3, 7, 8,12, 4, 598, 12, 4, 7, 9, 1, 8, 2,11, 6, 3,10, 599, 4,12, 8, 7, 3, 2, 9,10,11, 6, 1, 5100, 7, 9,11, 4, 6, 8, 3,10, 2,12, 1, 5101, 8, 9, 2, 6, 3, 7,11, 4,12, 1,10, 5102, 3, 9, 2, 8, 6,12, 4, 1, 7,11,10, 5103, 10, 1,12, 9, 6, 2, 3,11, 7, 4, 8, 5104, 4, 3, 8, 7,12, 2, 9, 1,11, 6,10, 5105, 9, 5,11, 2,10, 1,12, 7, 8, 3, 4, 6106, 3,11, 5, 2,10, 7,12, 1, 8, 9, 4, 6107, 2, 9, 7, 3,12, 5,11, 1, 8,10, 4, 6108, 5, 9, 7,10, 2, 1, 8,11,12, 3, 4, 6109, 5, 1, 9, 8,12, 7, 2, 3, 4,11,10, 6110, 7,11, 1, 3, 5,10,12, 2, 9, 4, 8, 6111, 7, 3, 9, 5,11,10, 2, 4, 1,12, 8, 6112, 1, 9, 3,11, 5,10, 2, 4, 7,12, 8, 6113, 7, 2,10,12, 5, 1, 3,11, 9, 4, 8, 6114, 1,11, 4,12, 2, 7, 3, 8, 9,10, 5, 6115, 12, 2, 8, 3, 9,11, 4, 5, 1, 7,10, 6116, 9, 4, 5,12, 1, 6, 3,11, 8, 2,10, 7117, 1, 5, 4,11, 9, 3, 8, 2,12, 6,10, 7118, 8,12, 4, 5, 1, 6,11,10, 9, 2, 3, 7119, 4,11, 5, 1,10, 8,12, 2, 6, 9, 3, 7120, 10, 6,12, 2, 8, 3, 9,11, 4, 5, 1, 7121, 1,12, 4,11, 2, 5, 6, 9,10, 8, 3, 7122, 1, 9, 6, 5,11, 3,12, 2,10, 8, 4, 7123, 11, 1,10, 9, 5, 3, 4,12, 6, 2, 8, 7124, 12, 1,10, 2,11, 5, 9, 6, 4, 3, 8, 7125, 12, 2, 9, 1,11, 6,10, 5, 4, 3, 8, 7126, 2, 4,10,12, 8, 3, 1, 9, 6,11, 5, 7127, 2,12, 4,11, 1, 6, 5,10, 9, 8, 3, 7128, 9, 1,10,11, 5, 3, 2,12, 6, 4, 8, 7129, 3, 2, 9,10,11, 6, 1, 5, 4,12, 8, 7130, 10, 9, 2, 1, 6,12,11, 3, 5, 4, 8, 7131, 7,11, 3, 6, 2, 5,12, 9,10, 1, 4, 8132, 2,11, 3,12, 1, 6, 5,10, 9, 7, 4, 8133, 9, 2, 6,12, 3, 7, 1,11, 5, 4,10, 8134, 3, 2, 6,12, 9, 1, 7, 5,11, 4,10, 8135, 2,11, 6, 3,10, 5,12, 4, 7, 9, 1, 8136, 4, 6,11, 7, 9, 5, 3,10, 2,12, 1, 8137, 7,12, 5, 4, 3,11, 6,10, 2, 9, 1, 8138, 3,10, 7, 2,11, 5,12, 4, 6, 9, 1, 8139, 7, 3, 5, 4,12,11, 6, 1, 2, 9,10, 8140, 3, 7, 1,12, 4,11, 2, 5, 6, 9,10, 8141, 4, 7, 1, 9, 6, 5,11, 3,12, 2,10, 8142, 4,10, 1, 9, 3, 5,11, 6,12, 2, 7, 8143, 10, 9, 2, 1, 6,11,12, 4, 5, 3, 7, 8144, 11, 2, 9, 1,12, 6,10, 5, 3, 4, 7, 8145, 11, 1,10, 2,12, 5, 9, 6, 3, 4, 7, 8146, 4, 1,10, 9,12, 5, 2, 6, 3,11, 7, 8147, 2,10, 1,11, 3, 5, 9, 6,12, 4, 7, 8148, 1, 9, 2,10, 6,11, 3, 4, 5,12, 7, 8149, 12, 6, 9, 1, 7, 5,11,10, 4, 2, 3, 8150, 2, 6, 9,11, 7, 5, 1,10, 4,12, 3, 8151, 8,10, 6, 5, 3, 4,11,12, 7, 2, 1, 9152, 2,10, 6,11, 3, 4, 5,12, 7, 8, 1, 9153, 7, 4,12, 5,10, 3, 6,11, 2, 8, 1, 9154, 3,11, 5,10, 2, 4, 7,12, 8, 6, 1, 9155, 3,11, 5, 4, 8,10, 7, 6, 2,12, 1, 9156, 5, 7, 6,11, 3, 1, 8,12,10, 2, 4, 9157, 5, 7, 6, 2,12,10, 8, 3, 1,11, 4, 9158, 6, 5, 2,12, 3,11, 1, 8, 4, 7,10, 9159, 12, 5, 2, 6, 3,11, 7, 8, 4, 1,10, 9160, 1, 8, 2,11, 6, 3,10, 5,12, 4, 7, 9161, 2, 8, 4,10, 6, 1,11, 7,12, 3, 5, 9162, 4, 2,10,12, 8, 1, 3,11, 6, 7, 5, 9163, 5, 6, 4,12, 3, 2, 8,10,11, 1, 7, 9164, 2, 1, 6,12,11, 3, 5, 4, 8, 7,10, 9165, 6, 5, 2,11, 4,12, 1, 7, 3, 8,10, 9166, 5, 3, 4,12, 6, 2, 8, 7,11, 1,10, 9167, 2, 1, 6,11,12, 4, 5, 3, 7, 8,10, 9168, 6, 4,12, 5,11, 2, 7,10, 3, 8, 1, 9169, 6,11, 5, 7, 2, 4,10,12, 8, 3, 1, 9170, 8, 1, 6, 5,12, 4,11, 3, 7, 2,10, 9171, 2, 4, 6, 8,12, 1,11, 3,10, 5, 7, 9172, 2, 8, 6,12, 4, 1, 7,11,10, 5, 3, 9173, 8, 2,12, 6,10, 1, 7,11, 4, 5, 3, 9174, 7, 4, 1,12, 3, 8, 5, 9, 6, 2,10,11175, 6, 7, 5, 9, 4, 2,10,12, 8, 1, 3,11176, 4, 9, 5, 7, 6, 2,12,10, 8, 3, 1,11177, 4,12, 2, 7, 3, 8, 9,10, 5, 6, 1,11178, 8, 2,10, 7, 9, 4, 5,12, 1, 6, 3,11179, 5, 2,10, 7,12, 1, 8, 9, 4, 6, 3,11180, 7, 1,10, 6,12, 2, 8, 9, 3, 5, 4,11181, 1, 3, 8,10,12, 2, 6, 7, 5, 9, 4,11182, 12, 3, 4, 6, 5, 9, 7,10, 2, 1, 8,11183, 12, 3, 4, 5, 6,10, 7, 9, 1, 2, 8,11184, 2, 8, 1, 9, 7, 4,12, 5,10, 3, 6,11185, 12, 4, 5, 3, 7, 8,10, 9, 2, 1, 6,11186, 1, 7, 2, 8,10, 4,12, 3, 9, 5, 6,11187, 7, 4, 8, 5,10, 1,12, 9, 6, 2, 3,11188, 6,10, 2, 9, 1, 8, 7,12, 5, 4, 3,11189, 2, 5, 6, 9,10, 8, 3, 7, 1,12, 4,11190, 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, 1,9,8,10,6,5,3,4,11,12,7,22, 1,9,7,10,6,5,4,3,12,11,8,23, 1,6,5,10,9,6,3,7,2,12,4,114, 1,6,5,10,9,7,4,8,2,11,3,125, 1,10,9,8,7,3,6,4,12,11,5,26, 1,10,9,7,8,4,6,3,11,12,5,27, 1,8,4,7,10,9,6,5,2,12,3,118, 1,7,3,8,10,9,6,5,2,11,4,129, 1,9,6,11,5,7,2,4,10,12,8,310,1,11,4,9,5,7,6,2,12,10,8,311,1,5,7,11,9,6,2,8,3,12,4,1012,1,5,7,9,11,4,6,8,3,10,2,1213,1,11,7,6,8,4,9,2,12,10,5,314,1,8,4,6,11,7,9,5,3,10,2,1215,1,8,2,11,6,3,10,5,12,4,7,916,1,6,3,11,8,2,10,7,9,4,5,1217,1,8,11,7,10,2,6,5,9,12,3,418,1,8,3,10,7,2,11,5,12,4,6,919,1,10,2,7,8,11,6,3,4,12,5,920,1,7,2,10,8,3,11,6,9,4,5,1221,1,12,3,8,5,9,6,2,10,11,7,422,1,5,9,8,12,3,6,7,4,11,2,1023,1,8,2,12,5,3,9,7,11,4,6,1024,1,5,3,12,8,2,9,6,10,4,7,1125,1,12,8,6,7,3,9,5,11,10,2,426,1,6,2,12,7,3,9,5,11,4,8,1027,1,7,3,12,6,2,9,8,10,4,5,1128,1,7,3,6,12,8,9,2,4,10,5,1129,1,6,11,10,9,2,3,7,8,12,4,530,1,10,7,6,9,2,11,3,12,8,4,531,1,9,2,10,6,11,3,4,5,12,7,832,1,9,2,6,10,7,11,4,5,8,3,1233,1,7,10,6,12,2,8,3,9,11,4,534,1,7,4,12,6,8,2,3,9,11,10,535,1,6,8,12,7,4,2,10,5,11,3,936,1,12,2,6,7,10,8,4,5,11,3,937,1,7,4,8,10,2,12,3,11,5,6,938,1,10,4,8,7,2,12,6,11,5,3,939,1,7,2,8,10,4,12,3,9,5,6,1140,1,10,2,8,7,4,12,6,9,5,3,1141,2,10,8,9,5,6,3,4,11,12,7,142,2,10,7,9,5,6,4,3,12,11,8,143,2,9,10,8,7,3,5,4,12,11,6,144,2,9,10,7,8,4,5,3,11,12,6,145,2,11,4,7,6,10,5,1,9,12,8,346,2,8,4,10,6,7,5,1,12,9,11,347,2,6,4,10,8,1,11,5,12,3,7,948,2,8,4,10,6,1,11,7,12,3,5,949,2,12,6,4,8,7,9,1,10,11,5,350,2,5,4,12,7,1,9,8,10,3,6,1151,2,7,12,8,9,1,5,6,10,11,4,352,2,7,4,9,8,1,12,6,11,3,5,1053,2,9,7,5,10,3,11,1,12,8,6,454,2,9,3,5,10,11,7,1,4,12,6,855,2,6,5,11,7,1,9,10,8,4,3,1256,2,6,4,8,10,3,11,1,12,5,9,757,2,6,3,11,7,8,4,1,10,9,12,558,2,6,3,7,11,4,12,1,10,5,8,959,3,11,9,4,8,6,7,2,10,12,5,160,3,11,6,7,5,9,4,2,10,12,8,161,3,9,11,6,8,2,7,4,12,10,5,162,3,8,10,4,11,5,7,1,9,12,6,263,3,11,7,4,8,5,10,1,12,9,6,264,3,5,4,11,7,1,10,6,12,2,8,965,3,7,4,11,5,1,10,8,12,2,6,966,3,12,4,6,5,9,7,1,11,10,8,267,3,5,4,12,6,1,9,8,11,2,7,1068,3,8,12,6,9,1,7,5,11,10,4,269,3,6,4,9,8,1,12,7,10,2,5,1170,3,5,10,6,12,1,9,2,11,8,7,471,3,6,9,5,12,2,10,1,11,8,7,472,4,12,8,3,7,6,9,2,11,10,5,173,4,3,5,9,10,1,11,7,8,2,6,1274,4,7,11,5,10,1,9,3,12,8,6,275,4,5,10,6,11,1,9,2,12,7,8,376,4,6,9,5,11,2,10,1,12,7,8,377,5,7,12,4,10,2,8,3,11,9,6,178,5,6,11,3,12,4,8,1,9,10,7,279,5,3,6,7,11,1,12,4,10,2,8,980,6,5,12,4,11,3,7,2,10,9,8,1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 .