最小集合

northwolves

王守恩 发表于 2025-12-2 10:11
a (1) = 1, {1},
a (2) = 2, {1, 2},
a (5) = 3, {2, 3, 4},

{56,7,{1,4,7,19,27,28,29}}
{57,7,{2,5,8,20,28,29,30}}
{58,7,{3,6,9,21,29,30,31}}
{59,7,{4,7,10,22,30,31,32}}
{60,7,{5,8,11,23,31,32,33}}
{61,7,{6,9,12,24,32,33,34}}
{62,7,{1,7,22,25,33,34,35}}
{63,7,{2,8,23,26,34,35,36}}
{64,7,{3,9,24,27,35,36,37}}
{65,7,{4,10,25,28,36,37,38}}
{66,7,{5,11,26,29,37,38,39}}
{67,7,{6,12,27,30,38,39,40}}
{68,7,{7,13,28,31,39,40,41}}
{69,7,{8,14,29,32,40,41,42}}
{70,7,{9,15,30,33,41,42,43}}
{71,7,{10,16,31,34,42,43,44}}
{72,7,{11,17,32,35,43,44,45}}
{73,7,{12,18,33,36,44,45,46}}
{74,7,{13,19,34,37,45,46,47}}
{75,7,{14,20,35,38,46,47,48}}

王守恩

northwolves 发表于 2025-12-2 19:43
{56,7,{1,4,7,19,27,28,29}}
{57,7,{2,5,8,20,28,29,30}}
{58,7,{3,6,9,21,29,30,31}}

{70,7,{1,23,31,33,35,38,54}}——23+31=54——这是最大的——无端的猜测。
{71,7,{2,24,32,34,36,39,55}}
{72,7,{3,25,33,35,27,40,56}}
{73,7,{4,26,34,36,38,41,57}}
{74,7,{5,27,35,37,39,42,58}}
{75,7,{6,28,36,38,40,43,59}}——75有2个解。

{87,8,{1,11,18,29,32,54,55,56}}
{88,8,{2,12,19,30,33,55,56,57}}
{89,8,{3,13,20,31,34,56,57,58}}
{90,8,{4,14,21,32,35,57,58,59}}
{91,8,{5,15,22,33,36,58,59,60}}
{92,8,{6,16,23,34,37,59,60,61}}
{93,8,{7,17,24,35,38,60,61,62}}
{94,8,{8,18,25,36,39,61,62,63}}
{95,8,{9,19,26,37,40,62,63,64}}
{96,8,{10,20,27,38,41,63,64,65}}
{97,8,{11,21,28,39,42,64,65,66}}
{98,8,{12,22,29,40,43,65,66,67}}
{99,8,{13,23,30,41,44,66,67,68}}
{100,8,{14,24,31,42,45,67,68,69}}
{101,8,{15,25,32,43,46,68,69,70}}
{102,8,{16,26,33,44,47,69,70,71}}
{103,8,{17,27,34,45,48,70,71,72}}
{104,8,{18,28,35,46,49,71,72,73}}
{105,8,{19,29,36,47,50,72,73,74}}——105只有1个解？

王守恩

aimisiyou 发表于 2025-11-26 08:56
K=9,(12 14 17 20 21 31 50 70 90)
K=9,(10 29 48 57 59 62 65 66 86)

{91,9,{1,20,39,48,50,53,56,57,77}}
{92,9,{2,21,40,49,51,54,57,58,78}}
{93,9,{3,22,41,50,52,55,58,59,79}}
{94,9,{4,23,42,51,53,56,59,60,80}}
{95,9,{5,24,43,52,54,57,60,61,81}}
{96,9,{6,25,44,53,55,58,61,62,82}}
{97,9,{7,26,45,54,56,59,62,63,83}}
{98,9,{8,27,46,55,57,60,63,64,84}}
{99,9,{9,28,47,56,58,61,64,65,85}}
{100,9,{10,29,48,57,59,62,65,66,86}}
{101,9,{11,23,49,58,60,63,66,67,87}}
{102,9,{12,31,50,59,61,64,67,68,88}}

{89,9,{1,3,6,9,10,20,39,59,79},9,90}
{90,9,{2,4,7,10,11,21,40,60,80},9,91}
{91,9,{3,5,8,11,12,22,41,61,81},9,92}
{92,9,{4,6,9,12,13,23,42,62,82},9,93}
{93,9,{5,7,10,13,14,24,43,63,83},9,94}
{94,9,{6,8,11,14,15,25,44,64,84},9,95}
{95,9,{7,9,12,15,16,26,45,65,85},9,96}
{96,9,{8,10,13,16,17,27,46,66,86},9,97}
{97,9,{9,11,14,17,18,28,47,67,87},9,98}
{98,9,{10,12,15,18,19,29,48,68,88},9,99}
{99,9,{11,13,16,19,20,30,49,69,89},9,100}
{100,9,{12,14,17,20,21,31,50,70,90},9,101}
{101,9,{13,15,18,21,22,32,51,71,91},9,102}

王守恩

继续整理。

只能利用——帖子《求{1, 2, ..., 100}没有等和对的最大子集》里面的数字串——谢谢mathe！！！

a (1) = 1, {1},
a (2) = 2, {1, 2},
a (5) = 3, {2, 3, 4},
a (13) = 4, {3, 5, 6, 10}
a (28) = 5, {7, 14, 15, 18, 20}
a (49) = 6, {12, 17, 24, 26, 34, 35}
a (75) = 7, {14, 20, 35, 38, 46, 47, 48}, {6, 28, 36, 38, 40, 43, 59}——75 有2个解。
a (105) = 8, {19, 29, 36, 47, 50, 72, 73, 74}——105 只有1个解？
a (129) = 9, {28, 36, 48, 50, 73, 79, 80, 90, 106}
a (161) = 10, {46, 47, 59, 74, 78, 89, 92, 94, 118, 128}
a (195) = 11, {41, 56, 59, 82, 86, 90, 102, 121, 126, 140, 154}
a (217) = 12, {54, 62, 77, 99, 104, 105, 106, 138, 154, 163, 184, 201}
a (259) = 13, {54, 69, 85, 94, 101, 103, 105, 147, 148, 171, 177, 185, 212}
a (333) = 14, {19, 31, 76, 100, 124, 125, 126, 162, 208, 213, 216, 222, 235, 287}
a (405) = 15, {32, 93, 118, 126, 130, 134, 141, 148, 223, 225, 244, 254, 263, 289, 306}

northwolves

75 有14个解:
{{5,30,34,36,41,44,60},{6,28,36,38,40,43,59},{7,31,35,37,42,45,60},{9,32,36,38,43,46,60},{9,36,39,43,44,45,60},{14,20,35,38,46,47,48},{16,21,36,43,46,47,60},{16,29,30,33,40,55,60},{18,22,35,40,41,49,56},{18,25,33,34,39,52,56},{19,23,36,41,42,50,57},{19,26,34,35,40,53,57},{20,24,37,42,43,51,58},{20,27,35,36,41,54,58}}

王守恩

手工理一理方法。譬如。

先有第1行。再斜着走——2+55——3+56——4+57——5+58——

关键是第1列。

{87,8,{1,11,18,29,32,54,55,56}},2+55,3+54,4+29,5+56,
{88,8,{2,12,19,30,33,55,56,57}},1+57,3+56,4+55,5+30,6+57,
{89,8,{3,13,20,31,34,56,57,58}},1+58,2+58,4+57,5+56,6+31,7+58,
{90,8,{4,14,21,32,35,57,58,59}},1+36,2+59,3+59,5+58,6+57,7+32,8+59,
{91,8,{5,15,22,33,36,58,59,60}},1+37,
{92,8,{6,16,23,34,37,59,60,61}},1+60,
{93,8,{7,17,24,35,38,60,61,62}},1+61,
{94,8,{8,18,25,36,39,61,62,63}},1+63,
{95,8,{9,19,26,37,40,62,63,64}},1+62,
{96,8,{10,20,27,38,41,63,64,65}},1+64,
{97,8,{11,21,28,39,42,64,65,66}},1+66,
{98,8,{12,22,29,40,43,65,66,67}}
{99,8,{13,23,30,41,44,66,67,68}}
{100,8,{14,24,31,42,45,67,68,69}}
{101,8,{15,25,32,43,46,68,69,70}}
{102,8,{16,26,33,44,47,69,70,71}}
{103,8,{17,27,34,45,48,70,71,72}}
{104,8,{18,28,35,46,49,71,72,73}}
{105,8,{19,29,36,47,50,72,73,74}}——105只有1个解？

王守恩

northwolves 发表于 2025-12-5 06:27
75 有14个解:
{{5,30,34,36,41,44,60},{6,28,36,38,40,43,59},{7,31,35,37,42,45,60},{9,32,36,38,43,46,60 ...

75 有14个解——太多了。79 就没有14个解了——{9, 34, 38, 40, 45, 48, 64}

northwolves

王守恩 发表于 2025-12-6 09:47
75 有14个解——太多了。79 就没有14个解了——{9, 34, 38, 40, 45, 48, 64}

79 有4个解:  {{9,34,38,40,45,48,64},{10,36,37,41,44,50,65},{12,30,38,41,43,47,66},{12,33,36,42,43,47,65}}

王守恩

northwolves 发表于 2025-12-7 08:54
79 有4个解:  {{9,34,38,40,45,48,64},{10,36,37,41,44,50,65},{12,30,38,41,43,47,66},{12,33,36,42,43, ...

79 有4个解——往前走不了, 试试往后退 ——第1个数总能退回到"1" 。

{01,26,30,32,37,40,56},2+56,
{02,27,31,33,38,41,57},1+57,
{03,28,32,34,39,42,58},1+34,
{04,29,33,35,40,43,59},1+43,
{05,30,34,36,41,44,60},1+34,
{06,31,35,37,42,45,61},1+42,
{07,32,36,38,43,46,62},1+38,
{08,33,37,39,44,47,63},1+37,
{09,34,38,40,45,48,64},1+48,——{9,34,38,40,45,48,64},
{10,35,39,41,46,49,65},1+??,

{01,27,28,32,35,41,56},2+27,
{02,28,29,33,36,42,57},1+29,
{03,29,30,34,37,43,58},1+58,
{04,30,31,35,38,44,59},1+38,
{05,31,32,36,39,45,60},1+36,
{06,32,33,37,40,46,61},1+37,
{07,33,34,38,41,47,62},1+47,
{08,34,35,39,42,48,63},1+42,
{09,35,36,40,43,49,64},1+43,
{10,36,37,41,44,50,65},1+50,——{10,36,37,41,44,50,65},
{11,37,38,42,45,51,66},1+??,

{01,19,27,30,32,36,55},2+55,
{02,20,28,31,33,37,56},1+56,
{03,21,29,32,34,38,57},1+34,
{04,22,30,33,35,39,58},1+33,
{05,23,31,34,36,40,59},1+40,
{06,24,32,35,37,41,60},1+60,
{07,25,33,36,38,42,61},1+42,
{08,26,34,37,39,43,62},1+62,
{09,27,35,38,40,44,63},1+35,
{10,28,36,39,41,45,64},1+45,
{11,29,37,40,42,46,65},1+65,
{12,30,38,41,43,47,66},1+41,——{12,30,38,41,43,47,66},
{13,31,39,42,44,48,67},1+??,

{01,22,25,31,32,36,54},2+54,
{02,23,26,32,33,37,55},1+55,
{03,24,27,33,34,38,56},1+56,
{04,25,28,34,35,39,57},1+28,
{05,26,29,35,36,40,58},1+36,
{06,27,30,36,37,41,59},1+41,
{07,28,31,37,38,42,60},1+37,
{08,29,32,38,39,43,61},1+39,
{09,30,33,39,40,44,62},1+62,
{10,31,34,40,41,45,63},1+40,
{11,32,35,41,42,46,64},1+42,
{12,33,36,42,43,47,65},1+47,——{12,33,36,42,43,47,65},
{13,34,37,43,44,48,66},1+??,

我们就找第1个数固定 = "1" 时的规律——把这些"1"都列出来——我还是不知道21#的代码怎么改。

王守恩

northwolves 发表于 2025-12-7 08:54
79 有4个解:  {{9,34,38,40,45,48,64},{10,36,37,41,44,50,65},{12,30,38,41,43,47,66},{12,33,36,42,43, ...

79 有4个解。譬如 ——{9,34,38,40,45,48,64}

64,{01,17,20,25,27,31,56},——64的时候就可以知道能到达79。
65,{02,18,21,26,28,32,57},
66,{03,19,22,27,29,33,58},
67,{04,20,23,28,30,34,59},
68,{05,21,24,29,31,35,60},
69,{06,22,25,30,32,36,61},
70,{07,23,26,31,33,37,62},
71,{08,24,27,32,34,38,63},
72,{09,25,28,33,35,39,64},
73,{10,26,29,34,36,40,65},
74,{11,27,30,35,37,41,66},
75,{12,28,31,36,38,42,67},
76,{13,29,32,37,39,43,68},
77,{14,30,33,38,40,44,69},
78,{15,31,34,39,41,45,70},
79,{16,32,35,40,42,46,71},——{9,34,38,40,45,48,64}的补集。