这样的数组有多少？

mathe

十进制小数点后20位计算精度结果(不允许互为余角，不允许45度角):
count[4]=38
count[6]=66
count[8]=730
count[10]=2200
count[12]=8962
count[14]=29388
count[16]=80554
count[18]=204580
count[20]=426774
count[22]=657044
count[24]=758292
count[26]=696840
count[28]=554264
count[30]=397156
count[32]=248996
count[34]=125440
count[36]=53628
count[38]=20352
count[40]=8360

王守恩

看来这8项的方案不光是用这19个“1”。
01: {1, 59, 61, 87}=18-0
02: {2, 58, 62, 84}=17-0
03: {3, 39, 75, 81}=16-5
04: {3, 57, 63, 81}=15-4
05: {3, 63, 69, 75}=14-3
06: {4, 56, 64, 78}=13-2
07: {5, 55, 65, 75}=12-1
08: {6, 42, 66, 78}=11-2
09: {6, 54, 66, 72}=10-2
10: {7, 53, 67, 69}=09-2
11: {8, 52, 66, 68}=08-0
12: {9, 33, 69, 75}=07-1
13: {9, 51, 63, 69}=06-2
14: {10, 50, 60, 70}=5-0
15: {11, 49, 57, 71}=4-0
16: {12, 48, 54, 72}=3-1
17: {13, 47, 51, 73}=2-1
18: {14, 46, 48, 74}=1-0
19: {15, 51, 57, 63}

这8项的方案与40项的方案有联系,  8+40*2=88。
这12项的方案与38项的方案有联系,12+38*2=88。
这16项的方案与36项的方案有联系,16+36*2=88。

6项好不容易找了1个, tan(2)*tan(54)*tan(58)*tan(62)*tan(66)*tan(72)=1
倒过来是另一个, tan(18)*tan(24)*tan(28)*tan(32)*tan(36)*tan(88)=1
关键是得找33个(目标已有)。 这33个与19个又是该怎么联系？

northwolves

6项    {1, 57, 59, 61, 63, 81}, {9, 27, 29, 31, 33, 89}, {4, 48, 54, 56, 64, 72}

王守恩

northwolves 发表于 2024-3-27 23:01
6项    {1, 57, 59, 61, 63, 81}, {9, 27, 29, 31, 33, 89}, {4, 48, 54, 56, 64, 72}

01: {1, 59, 61, 87}
02: {2, 58, 62, 84}
03: {3, 39, 75, 81}
04: {3, 57, 63, 81}
05: {3, 63, 69, 75}
06: {4, 56, 64, 78}
07: {5, 55, 65, 75}
08: {6, 42, 66, 78}
09: {6, 54, 66, 72}
10: {7, 53, 67, 69}
11: {8, 52, 66, 68}
12: {9, 33, 69, 75}
13: {9, 51, 63, 69}
14: {10, 50, 60, 70}
15: {11, 49, 57, 71}
16: {12, 48, 54, 72}
17: {13, 47, 51, 73}
18: {14, 46, 48, 74}
19: {15, 51, 57, 63}
用这19个解(4项=19个解)只能折腾出13个解(6项=33个解)来？ 约定最小数+最大数<89
03+07={3, 39, 75, 81}+{5, 55, 65, 75}={3, 39, 81, 85, 35, 25}={3, 25, 35, 39, 81, 85}
04+15={3, 57, 63, 81}+{11, 49, 57, 71}={3, 63, 81,79, 41,19}={3, 19, 41, 63, 79, 81}
06+08={4, 34, 52, 56, 64, 84}
05+10={3, 23, 37, 63, 75, 83}
07+12={5, 21, 55, 57, 65, 81}
08+11={6, 22, 38, 42, 78, 82}
09+11={6, 22, 38, 54, 72, 82}
10+12={7, 15, 47, 53, 67, 81}
10+13={7, 27, 39, 53, 67, 81}
13+17={9, 19, 43, 63, 89, 77}
15+19={11, 27, 39, 49, 71, 75}
16+18={12, 26, 44, 54, 72, 76}
17+19={13, 27, 33, 47, 73, 75}

王守恩

northwolves 发表于 2024-3-24 11:08
楼主证明以下几个即可：{{3, 39, 75, 81}, {3, 63, 69, 75}, {6, 42, 66, 78}, {9, 15, 51, 87}, {9, 33, 6 ...

未证: {3, 39, 75, 81}只需证: {39,75}={57,63}
已证: {3, 57, 63, 81}
已证: {3, 57, 81, 63}
未证: {3, 69, 75, 63}只需证: {57,81}={69,75}

未证: {6, 42, 78, 66}
已证: {6, 54, 72, 66}只需证: {42,78}={54,72}

未证: {09, 33, 75, 69}只需证: {33,75}={51,63}
已证: {09, 51, 63, 69}
已证: {51, 09, 69, 63}
未证: {51, 15, 57, 63}只需证: {09,69}={15,57}

mathe

[6]10,16,20,52,56,88
[6]10,26,40,46,62,82
[6]11,25,35,47,61,83
[6]11,27,39,49,71,75
[6]12,16,24,44,76,84
[6]12,16,44,54,72,76
[6]12,24,28,32,48,88
[6]13,21,27,47,73,81
[6]13,23,25,49,59,85
[6]13,23,49,55,59,75
[6]13,27,33,47,73,75
[6]1,35,37,71,73,85
[6]1,37,65,71,73,75
[6]1,39,59,61,75,81
[6]14,18,36,46,74,78
[6]14,20,22,50,58,86
[6]15,17,19,25,53,89
[6]15,17,43,57,63,77
[6]15,19,21,41,79,81
[6]15,19,41,51,63,79
[6]15,21,27,29,31,89
[6]15,31,35,41,67,77
[6]1,57,59,61,63,81
[6]1,59,61,63,69,75
[6]18,24,28,32,36,88
[6]18,26,34,36,42,86
[6]2,34,38,70,74,80
[6]2,42,58,62,66,78
[6]25,27,33,35,39,85
[6]2,54,58,62,66,72
[6]3,13,47,73,75,81
[6]3,19,41,63,79,81
[6]3,23,37,63,75,83
[6]3,25,35,39,81,85
[6]3,25,35,63,69,85
[6]4,24,48,56,64,84
[6]4,32,40,68,70,76
[6]4,48,54,56,64,72
[6]5,11,47,61,75,83
[6]5,17,19,53,55,89
[6]5,21,27,55,65,87
[6]5,21,55,57,65,81
[6]5,31,41,65,67,77
[6]5,51,55,57,63,65
[6]5,9,51,55,65,87
[6]6,14,46,66,74,78
[6]6,22,38,42,78,82
[6]6,22,38,54,72,82
[6]6,26,34,42,66,86
[6]7,15,27,53,67,87
[6]7,15,29,43,79,85
[6]7,15,53,57,67,81
[6]7,27,39,53,67,81
[6]7,29,43,55,65,79
[6]8,12,48,52,68,84
[6]8,18,36,52,68,84
[6]8,28,44,50,64,80
[6]9,11,27,49,71,87
[6]9,11,49,69,71,75
[6]9,15,17,43,77,87
[6]9,15,29,31,51,89
[6]9,17,43,63,69,77
[6]9,23,33,37,75,83
[6]9,23,37,51,63,83
[6]9,25,33,35,69,85
[6]9,27,29,31,33,89
[8]10,11,49,50,57,60,70,71
[8]10,12,16,20,26,52,86,88
[8]10,12,24,48,50,60,70,84
[8]10,12,26,34,50,60,70,86
[8]10,12,48,50,54,60,70,72
[8]10,13,47,50,51,60,70,73
[8]10,14,20,46,48,52,56,88
[8]10,14,46,48,50,60,70,74
[8]10,15,21,27,50,60,70,87
[8]10,15,21,50,57,60,70,81
[8]10,15,25,35,50,60,70,85
[8]10,15,50,51,57,60,63,70
[8]10,16,20,22,24,56,82,88
[8]10,16,20,52,56,58,62,84
[8]10,16,26,40,42,62,76,82
[8]10,16,42,44,50,60,70,76
[8]10,17,39,43,50,60,70,77
[8]10,18,24,36,50,60,70,84
[8]10,18,36,42,50,60,70,78
[8]10,19,33,41,50,60,70,79
[8]10,21,23,37,50,60,70,83
[8]10,21,27,39,50,60,70,81
[8]10,22,24,38,50,60,70,82
[8]10,26,40,46,52,62,66,68
[8]10,27,33,39,50,60,70,75
[8]1,10,50,59,60,61,70,87
[8]11,12,24,48,49,57,71,84
[8]11,12,26,34,49,57,71,86
[8]11,12,48,49,54,57,71,72
[8]11,13,25,27,47,49,53,89
[8]11,13,27,47,49,71,73,75
[8]11,13,47,49,51,57,71,73
[8]11,14,46,48,49,57,71,74
[8]1,11,49,57,59,61,71,87
[8]11,15,17,25,49,53,57,89
[8]11,15,21,27,49,57,71,87
[8]11,15,25,35,49,57,71,85
[8]11,15,31,35,57,67,71,77
[8]11,16,42,44,49,57,71,76
[8]11,17,25,27,39,49,53,89
[8]11,17,25,35,39,61,77,83
[8]11,17,39,43,49,57,71,77
[8]11,18,24,36,49,57,71,84
[8]11,18,36,42,49,57,71,78
[8]11,20,30,40,49,57,71,80
[8]11,21,23,37,49,57,71,83
[8]11,21,27,39,49,57,71,81
[8]11,22,24,38,49,57,71,82
[8]1,12,24,48,59,61,84,87
[8]1,12,26,34,59,61,86,87
[8]1,12,48,54,59,61,72,87
[8]11,25,27,35,39,49,71,85
[8]11,25,35,47,53,61,67,69
[8]11,27,31,35,39,67,71,77
[8]11,27,31,35,47,67,71,73
[8]1,13,47,51,59,61,73,87
[8]1,13,47,59,61,73,75,81
[8]1,14,46,48,59,61,74,87
[8]1,15,21,57,59,61,81,87
[8]1,15,25,35,59,61,85,87
[8]1,15,35,41,61,67,77,87
[8]1,15,51,57,59,61,63,87
[8]1,16,42,44,59,61,76,87
[8]1,17,39,43,59,61,77,87
[8]1,18,24,36,59,61,84,87
[8]1,18,36,42,59,61,78,87
[8]1,19,33,41,59,61,79,87
[8]1,19,41,59,61,63,79,81
[8]1,20,30,40,59,61,80,87
[8]1,21,23,37,59,61,83,87
[8]1,21,27,37,65,71,73,87
[8]1,21,27,39,59,61,81,87
[8]12,13,24,47,48,51,73,84
[8]12,13,26,34,47,51,73,86
[8]12,13,47,48,51,54,72,73
[8]1,21,37,41,65,73,79,81
[8]1,21,37,57,65,71,73,81
[8]12,14,26,34,46,48,74,86
[8]12,15,21,24,27,48,84,87
[8]12,15,21,24,48,57,81,84
[8]12,15,21,26,27,34,86,87
[8]12,15,21,26,34,57,81,86
[8]12,15,21,27,48,54,72,87
[8]12,15,21,48,54,57,72,81
[8]12,15,24,25,35,48,84,85
[8]12,15,24,48,51,57,63,84
[8]12,15,25,26,34,35,85,86
[8]12,15,25,35,48,54,72,85
[8]12,15,26,34,51,57,63,86
[8]12,15,48,51,54,57,63,72
[8]12,16,24,28,32,44,76,88
[8]12,16,26,34,42,44,76,86
[8]12,17,24,39,43,48,77,84
[8]12,17,26,34,39,43,77,86
[8]12,17,39,43,48,54,72,77
[8]12,18,24,26,34,36,84,86
[8]12,19,24,33,41,48,79,84
[8]12,19,26,33,34,41,79,86
[8]12,19,33,41,48,54,72,79
[8]12,20,24,30,40,48,80,84
[8]12,20,26,30,34,40,80,86
[8]12,20,30,40,48,54,72,80
[8]12,21,23,24,37,48,83,84
[8]12,21,23,26,34,37,83,86
[8]12,21,23,37,48,54,72,83
[8]12,21,24,27,39,48,81,84
[8]12,21,26,27,34,39,81,86
[8]12,21,27,39,48,54,72,81
[8]12,22,24,26,34,38,82,86
[8]12,22,24,38,48,54,72,82
[8]1,22,24,38,59,61,82,87
[8]12,24,27,33,39,48,75,84
[8]12,26,27,33,34,39,75,86
[8]12,26,32,34,40,68,70,76
[8]12,27,33,39,48,54,72,75
[8]1,23,37,43,59,63,79,85
[8]1,23,37,59,61,63,75,83
[8]1,25,35,39,59,61,81,85
[8]1,25,35,59,61,63,69,85
[8]1,2,58,59,61,62,84,87
[8]1,27,33,39,59,61,75,87
[8]13,14,46,47,48,51,73,74
[8]13,15,19,25,47,51,53,89
[8]13,15,21,27,47,51,73,87
[8]13,15,21,47,51,57,73,81
[8]13,15,25,35,47,51,73,85
[8]13,16,42,44,47,51,73,76
[8]13,18,24,36,47,51,73,84
[8]13,18,36,42,47,51,73,78
[8]13,19,21,23,55,59,79,81
[8]13,19,23,25,33,59,79,85
[8]13,19,23,33,55,59,75,79
[8]13,19,23,51,55,59,63,79
[8]13,19,25,27,33,47,53,89
[8]13,19,25,47,53,59,61,81
[8]13,19,33,41,47,51,73,79
[8]13,20,30,40,47,51,73,80
[8]13,21,23,27,29,49,55,89
[8]13,21,23,27,49,55,59,87
[8]13,21,23,37,47,51,73,83
[8]13,21,23,49,55,57,59,81
[8]13,22,24,38,47,51,73,82
[8]13,23,49,51,55,57,59,63
[8]13,25,27,33,35,47,73,85
[8]1,33,35,37,41,73,79,85
[8]1,33,37,41,65,73,75,79
[8]1,35,37,39,43,71,77,85
[8]1,35,37,41,61,63,77,83
[8]1,35,39,41,61,67,77,81
[8]1,35,41,47,61,67,73,81
[8]1,35,41,61,63,67,69,77
[8]1,37,39,43,65,71,75,77
[8]1,37,41,43,63,65,77,79
[8]1,37,41,51,63,65,73,79
[8]1,37,43,57,63,65,71,77
[8]1,37,51,57,63,65,71,73
[8]14,15,21,27,46,48,74,87
[8]14,15,21,46,48,57,74,81
[8]14,15,25,35,46,48,74,85
[8]14,15,46,48,51,57,63,74
[8]14,17,39,43,46,48,74,77
[8]14,18,24,36,46,48,74,84
[8]14,18,26,34,36,46,74,86
[8]14,19,33,41,46,48,74,79
[8]14,20,22,50,56,58,64,78
[8]14,20,30,40,46,48,74,80
[8]14,21,23,37,46,48,74,83
[8]14,21,27,39,46,48,74,81
[8]14,22,24,38,46,48,74,82
[8]14,27,33,39,46,48,74,75
[8]1,4,56,59,61,64,78,87
[8]15,16,21,27,42,44,76,87
[8]15,16,21,42,44,57,76,81
[8]15,16,25,35,42,44,76,85
[8]15,16,42,44,51,57,63,76
[8]15,17,19,21,23,25,83,89
[8]15,17,19,25,53,59,61,87
[8]15,17,19,41,43,63,77,79
[8]15,17,21,27,39,43,77,87
[8]15,17,21,39,43,57,77,81
[8]15,17,25,35,39,43,77,85
[8]15,18,21,24,27,36,84,87
[8]15,18,21,24,36,57,81,84
[8]15,18,21,27,36,42,78,87
[8]15,18,21,36,42,57,78,81
[8]15,18,24,25,35,36,84,85
[8]15,18,24,36,51,57,63,84
[8]15,18,25,35,36,42,78,85
[8]15,18,36,42,51,57,63,78
[8]15,19,21,27,33,41,79,87
[8]15,19,25,33,35,41,79,85
[8]15,20,21,27,30,40,80,87
[8]15,20,21,30,40,57,80,81
[8]15,20,25,30,35,40,80,85
[8]15,20,30,40,51,57,63,80
[8]15,21,22,24,27,38,82,87
[8]15,21,22,24,38,57,81,82
[8]15,21,23,25,35,37,83,85
[8]15,21,23,29,37,43,79,85
[8]15,21,23,37,51,57,63,83
[8]15,21,25,27,35,39,81,85
[8]15,21,31,35,37,41,77,83
[8]15,22,24,25,35,38,82,85
[8]15,22,24,38,51,57,63,82
[8]15,31,35,41,47,51,67,73
[8]1,5,41,61,65,67,77,87
[8]1,5,55,59,61,65,75,87
[8]16,17,39,42,43,44,76,77
[8]16,18,24,36,42,44,76,84
[8]16,19,33,41,42,44,76,79
[8]16,20,22,42,44,50,58,86
[8]16,20,30,40,42,44,76,80
[8]16,21,23,37,42,44,76,83
[8]16,21,27,39,42,44,76,81
[8]16,22,24,38,42,44,76,82
[8]16,27,33,39,42,44,75,76
[8]1,6,28,32,59,61,87,88
[8]1,6,42,59,61,66,78,87
[8]1,6,54,59,61,66,72,87
[8]1,7,13,59,73,79,81,85
[8]1,7,15,43,59,79,85,87
[8]17,18,24,36,39,43,77,84
[8]17,18,36,39,42,43,77,78
[8]17,19,23,25,59,61,63,83
[8]17,19,23,43,55,59,63,79
[8]17,19,25,27,33,39,53,89
[8]17,19,25,39,53,59,61,81
[8]17,19,25,53,59,61,63,69
[8]17,19,33,39,41,43,77,79
[8]17,20,30,39,40,43,77,80
[8]17,21,23,37,39,43,77,83
[8]17,22,24,38,39,43,77,82
[8]17,23,25,39,43,49,59,85
[8]17,23,39,43,49,55,59,75
[8]17,23,43,49,55,57,59,63
[8]1,7,27,65,67,71,73,87
[8]1,7,35,67,69,71,73,85
[8]1,7,39,43,59,79,81,85
[8]1,7,41,65,67,73,79,81
[8]1,7,43,55,59,65,79,87
[8]1,7,43,59,63,69,79,85
[8]1,7,53,59,61,67,69,87
[8]1,7,57,65,67,71,73,81
[8]1,7,65,67,69,71,73,75
[8]18,19,24,33,36,41,79,84
[8]18,19,33,36,41,42,78,79
[8]18,20,24,30,36,40,80,84
[8]18,20,30,36,40,42,78,80
[8]18,21,23,24,36,37,83,84
[8]18,21,23,36,37,42,78,83
[8]18,21,24,27,36,39,81,84
[8]18,21,27,36,39,42,78,81
[8]18,22,24,36,38,42,78,82
[8]18,24,27,33,36,39,75,84
[8]18,27,33,36,39,42,75,78
[8]1,8,52,59,61,66,68,87
[8]19,20,30,33,40,41,79,80
[8]19,21,23,33,37,41,79,83
[8]19,21,27,33,39,41,79,81
[8]19,22,24,33,38,41,79,82
[8]19,25,33,35,41,47,61,83
[8]1,9,33,59,61,69,75,87
[8]1,9,37,43,65,71,77,87
[8]1,9,37,51,65,71,73,87
[8]1,9,51,59,61,63,69,87
[8]20,21,23,30,37,40,80,83
[8]20,21,27,30,39,40,80,81
[8]20,22,24,30,38,40,80,82
[8]20,27,30,33,39,40,75,80
[8]2,10,50,58,60,62,70,84
[8]2,11,49,57,58,62,71,84
[8]21,22,23,24,37,38,82,83
[8]21,22,24,27,38,39,81,82
[8]2,12,26,34,58,62,84,86
[8]21,23,27,33,37,39,75,83
[8]21,23,29,37,43,55,65,79
[8]2,12,48,54,58,62,72,84
[8]21,27,29,31,37,65,71,73
[8]2,13,47,51,58,62,73,84
[8]2,14,46,48,58,62,74,84
[8]2,14,46,58,62,66,74,78
[8]2,15,21,27,58,62,84,87
[8]2,15,21,57,58,62,81,84
[8]2,15,25,35,58,62,84,85
[8]2,15,51,57,58,62,63,84
[8]2,16,42,44,58,62,76,84
[8]2,17,39,43,58,62,77,84
[8]2,18,36,42,58,62,78,84
[8]2,19,33,41,58,62,79,84
[8]2,20,30,40,58,62,80,84
[8]2,21,23,37,58,62,83,84
[8]2,21,27,39,58,62,81,84
[8]2,22,24,38,58,62,82,84
[8]2,22,38,42,58,62,78,82
[8]2,22,38,54,58,62,72,82
[8]22,24,27,33,38,39,75,82
[8]22,24,28,38,44,50,64,80
[8]2,26,34,42,58,62,66,86
[8]2,27,33,39,58,62,75,84
[8]2,3,29,31,58,62,84,89
[8]2,3,39,58,62,75,81,84
[8]2,34,38,42,44,70,76,80
[8]2,3,57,58,62,63,81,84
[8]2,3,58,62,63,69,75,84
[8]2,4,38,64,70,74,78,80
[8]2,4,40,62,68,70,76,84
[8]2,4,56,58,62,64,78,84
[8]2,5,55,58,62,65,75,84
[8]27,31,33,35,39,41,67,77
[8]27,31,33,35,41,47,67,73
[8]2,7,53,58,62,67,69,84
[8]2,8,34,66,68,70,74,80
[8]2,8,44,50,58,64,80,84
[8]2,8,52,58,62,66,68,84
[8]2,9,15,51,58,62,84,87
[8]2,9,27,33,58,62,84,87
[8]2,9,33,58,62,69,75,84
[8]2,9,51,58,62,63,69,84
[8]3,10,29,31,50,60,70,89
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[8]3,10,50,57,60,63,70,81
[8]3,10,50,60,63,69,70,75
[8]3,11,25,31,35,47,83,89
[8]3,11,29,31,49,57,71,89
[8]3,11,39,49,57,71,75,81
[8]3,11,49,57,63,69,71,75
[8]3,12,24,29,31,48,84,89
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[8]3,12,24,48,57,63,81,84
[8]3,12,24,48,63,69,75,84
[8]3,12,26,29,31,34,86,89
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[8]3,12,26,34,57,63,81,86
[8]3,12,26,34,63,69,75,86
[8]3,12,29,31,48,54,72,89
[8]3,12,39,48,54,72,75,81
[8]3,12,48,54,57,63,72,81
[8]3,12,48,54,63,69,72,75
[8]3,13,19,25,47,53,81,89
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[8]3,13,23,29,49,55,75,89
[8]3,13,25,35,47,73,81,85
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[8]3,13,47,51,57,63,73,81
[8]3,13,47,51,63,69,73,75
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[8]3,17,39,43,57,63,77,81
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[8]3,18,24,36,63,69,75,84
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[8]3,6,39,54,66,72,75,81
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[8]3,6,54,57,63,66,72,81
[8]3,6,54,63,66,69,72,75
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[8]9,12,24,27,33,48,84,87
[8]9,12,24,33,48,69,75,84
[8]9,12,24,48,51,63,69,84
[8]9,12,26,27,33,34,86,87
[8]9,12,26,33,34,69,75,86
[8]9,12,26,34,51,63,69,86
[8]9,12,27,33,48,54,72,87
[8]9,12,33,48,54,69,72,75
[8]9,12,48,51,54,63,69,72
[8]9,13,23,29,49,51,55,89
[8]9,13,23,49,51,55,59,87
[8]9,13,27,33,47,51,73,87
[8]9,13,33,47,51,69,73,75
[8]9,14,15,46,48,51,74,87
[8]9,14,27,33,46,48,74,87
[8]9,14,33,46,48,69,74,75
[8]9,14,46,48,51,63,69,74
[8]9,15,16,42,44,51,76,87
[8]9,15,17,29,31,43,77,89
[8]9,15,18,24,36,51,84,87
[8]9,15,18,36,42,51,78,87
[8]9,15,19,33,41,51,79,87
[8]9,15,20,30,40,51,80,87
[8]9,15,21,23,37,51,83,87
[8]9,15,22,24,38,51,82,87
[8]9,15,25,27,33,35,85,87
[8]9,15,25,35,51,63,69,85
[8]9,16,27,33,42,44,76,87
[8]9,16,33,42,44,69,75,76
[8]9,16,42,44,51,63,69,76
[8]9,17,19,23,25,33,83,89
[8]9,17,19,25,33,53,69,89
[8]9,17,23,29,43,49,55,89
[8]9,17,23,37,43,63,77,83
[8]9,17,23,43,49,55,59,87
[8]9,17,27,33,39,43,77,87
[8]9,17,33,39,43,69,75,77
[8]9,18,24,27,33,36,84,87
[8]9,18,24,33,36,69,75,84
[8]9,18,24,36,51,63,69,84
[8]9,18,27,33,36,42,78,87
[8]9,18,33,36,42,69,75,78
[8]9,18,36,42,51,63,69,78
[8]9,19,33,41,51,63,69,79
[8]9,20,27,30,33,40,80,87
[8]9,20,30,33,40,69,75,80
[8]9,20,30,40,51,63,69,80
[8]9,21,23,27,33,37,83,87
[8]9,22,24,27,33,38,82,87
[8]9,22,24,33,38,69,75,82
[8]9,22,24,38,51,63,69,82
[8]9,23,25,33,35,37,83,85
[8]9,23,29,33,37,43,79,85
[8]9,23,29,37,43,49,71,85
[8]9,29,31,37,43,65,71,77
[8]9,29,31,37,51,65,71,73
[8]9,31,33,35,37,41,77,83
[8]9,31,33,35,41,67,69,77

王守恩

谢谢mathe!有这33个解, 6项与4项的关系就清晰了。
[01]: {01, 35, 37, 71, 73, 85},
[02]: {01, 37, 65, 71, 73, 75},
[03]: {01, 39, 59, 61, 75, 81},
[04]: {01, 57, 59, 61, 63, 81},
[05]: {01, 59, 61, 63, 69, 75},
[06]: {02, 34, 38, 70, 74, 80},
[07]: {02, 42, 58, 62, 66, 78},
[08]: {02, 54, 58, 62, 66, 72},
[09]: {03, 13, 47, 73, 75, 81},
[10]: {03, 19, 41, 63, 79, 81},
[11]: {03, 23, 37, 63, 75, 83},
[12]: {03, 25, 35, 39, 81, 85},
[13]: {03, 25, 35, 63, 69, 85},
[14]: {04, 24, 48, 56, 64, 84},
[15]: {04, 32, 40, 68, 70, 76},
[16]: {04, 48, 54, 56, 64, 72},
[17]: {05, 11, 47, 61, 75, 83},
[18]: {05, 21, 55, 57, 65, 81},
[19]: {05, 31, 41, 65, 67, 77},
[20]: {05, 51, 55, 57, 63, 65},
[21]: {06, 14, 46, 66, 74, 78},
[22]: {06, 22, 38, 42, 78, 82},
[23]: {06, 22, 38, 54, 72, 82},
[24]: {07, 15, 53, 57, 67, 81},
[25]: {07, 27, 39, 53, 67, 81},
[26]: {07, 29, 43, 55, 65, 79},
[27]: {08, 28, 44, 50, 64, 80},
[28]: {09, 11, 49, 69, 71, 75},
[29]: {09, 17, 43, 63, 69, 77},
[30]: {11, 27, 39, 49, 71, 75},
[31]: {12, 16, 44, 54, 72, 76},
[32]: {13, 23, 49, 55, 59, 75},
[33]: {13, 27, 33, 47, 73, 75},

mathe

计算机计算表示，只有下面这些是基础解

1. [4] 1, 59, 61, 87,
   
2. [4] 2, 58, 62, 84,
   
3. [4] 3, 63, 69, 75,
   
4. [4] 3, 57, 63, 81,
   
5. [4] 4, 56, 64, 78,
   
6. [4] 5, 55, 65, 75,
   
7. [4] 6, 54, 66, 72,
   
8. [4] 7, 53, 67, 69,
   
9. [4] 8, 52, 66, 68,
   
10. [4] 9, 51, 63, 69,
    
11. [4] 10, 50, 60, 70,
    
12. [4] 11, 49, 57, 71,
    
13. [4] 12, 48, 54, 72,
    
14. [4] 13, 47, 51, 73,
    
15. [4] 14, 46, 48, 74,
    
16. [4] 15, 51, 57, 63,
    
17. [4] 9, 15, 51, 87,
    
18. [4] 15, 21, 57, 81,
    
19. [4] 12, 24, 48, 84,
    
20. [6] 5, 11, 47, 61, 75, 83,
    
21. [6] 5, 17, 19, 53, 55, 89,
    
22. [6] 10, 16, 20, 52, 56, 88,
    
23. [6] 14, 20, 22, 50, 58, 86,
    
24. [6] 13, 23, 49, 55, 59, 75,
    
25. [6] 15, 17, 19, 25, 53, 89,
    
26. [6] 13, 23, 25, 49, 59, 85,
    
27. [6] 11, 25, 35, 47, 61, 83,
    
28. [6] 10, 26, 40, 46, 62, 82,
    
29. [8] 1, 7, 13, 59, 73, 79, 81, 85,
    
30. [8] 7, 13, 19, 53, 55, 59, 79, 81,
    
31. [8] 13, 19, 25, 47, 53, 59, 61, 81,
    
32. [8] 9, 11, 17, 23, 25, 49, 83, 89,
    
33. [8] 17, 19, 23, 25, 59, 61, 63, 83,
    
34. [8] 11, 13, 25, 27, 47, 49, 53, 89,
    
35. [8] 7, 13, 27, 29, 49, 71, 73, 85,
    
36. [8] 7, 13, 27, 29, 49, 53, 55, 89,
    
37. [8] 5, 11, 27, 31, 47, 53, 67, 89,
    
38. [8] 11, 27, 31, 35, 47, 67, 71, 73,
    
39. [8] 5, 19, 41, 47, 53, 61, 67, 81,
    
40. [8] 1, 35, 41, 47, 61, 67, 73, 81,
    

复制代码

然后我们可以通过拼接两个较短的解产生所有其它解
比如
[6] 11, 25, 35, 47, 61, 83,
[6] 10, 26, 40, 46, 62, 82,
它们没有公共元素，直接合并可以产生一个长度为12的解
[12] 11, 25, 35, 47, 61, 83, 80, 64, 50, 28, 8

又比如
[4] 3, 63, 69, 75,
[4] 3, 57, 63, 81,
有公共元，可以消除它们公共元并拼接成
[6] 63, 69, 75, 33, 27, 9

当然如果一个拼接方案产生的解长度没有增长，不计算在内。

王守恩

mathe 发表于 2024-3-28 19:31
计算机计算表示，只有下面这些是基础解

然后我们可以通过拼接两个较短的解产生所有其它解

当然如果一个拼接方案产生的解长度没有增长，不计算在内。
[1]=05, 17, 19, 53, 55, 89,
[2]=15, 17, 19, 25, 53, 89,
[3]=05, 55, 65, 75,
比较[1],[2]=比较[05,55],[15,25],  由[3]可知[05,55]=[15,25]。
[1]=05, 11, 47, 61, 75, 83,
[2]=11, 25, 35, 47, 61, 83,
[3]=05, 55, 65, 75,
比较[1],[2]=比较[05,75],[25,35],  由[3]可知[05,75]=[25,35]。
[1]=13, 23, 49, 55, 59, 75,
[2]=13, 23, 25, 49, 59, 85,
[3]=05, 55, 65, 75,
比较[1],[2]=比较[55,75],[25,85],  由[3]可知[55,75]=[25,85]。

思路很明确:充分利用4项基础解,让6项基础解尽可能的少(最好是0)。
第1步,扩。(4-1)+3=3+3=6，第2步,换。2个数换2个数。

王守恩

让6项基础解=0是不可能的。这题目就有点复杂了。
展望一下。
4项: 38/2-19(基础解)=0,  让4项基础解扩容也不可能。
6项: 66/2-9(基础解)=24, 24=3+3,
8项: 730/2-12(基础解)=353, 353=3+5=4+4,
10项: 2200/2-?=?, ?=3+7=4+6=5+5,
12项: 8962/2-?=?, ?=3+9=4+8=5+7=6+6,