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=38
count=66
count=730
count=2200
count=8962
count=29388
count=80554
count=204580
count=426774
count=657044
count=758292
count=696840
count=554264
count=397156
count=248996
count=125440
count=53628
count=20352
count=8360
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？
6项 {1, 57, 59, 61, 63, 81}, {9, 27, 29, 31, 33, 89}, {4, 48, 54, 56, 64, 72}
本帖最后由 王守恩 于 2024-3-28 09:35 编辑
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}
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}
10,16,20,52,56,88
10,26,40,46,62,82
11,25,35,47,61,83
11,27,39,49,71,75
12,16,24,44,76,84
12,16,44,54,72,76
12,24,28,32,48,88
13,21,27,47,73,81
13,23,25,49,59,85
13,23,49,55,59,75
13,27,33,47,73,75
1,35,37,71,73,85
1,37,65,71,73,75
1,39,59,61,75,81
14,18,36,46,74,78
14,20,22,50,58,86
15,17,19,25,53,89
15,17,43,57,63,77
15,19,21,41,79,81
15,19,41,51,63,79
15,21,27,29,31,89
15,31,35,41,67,77
1,57,59,61,63,81
1,59,61,63,69,75
18,24,28,32,36,88
18,26,34,36,42,86
2,34,38,70,74,80
2,42,58,62,66,78
25,27,33,35,39,85
2,54,58,62,66,72
3,13,47,73,75,81
3,19,41,63,79,81
3,23,37,63,75,83
3,25,35,39,81,85
3,25,35,63,69,85
4,24,48,56,64,84
4,32,40,68,70,76
4,48,54,56,64,72
5,11,47,61,75,83
5,17,19,53,55,89
5,21,27,55,65,87
5,21,55,57,65,81
5,31,41,65,67,77
5,51,55,57,63,65
5,9,51,55,65,87
6,14,46,66,74,78
6,22,38,42,78,82
6,22,38,54,72,82
6,26,34,42,66,86
7,15,27,53,67,87
7,15,29,43,79,85
7,15,53,57,67,81
7,27,39,53,67,81
7,29,43,55,65,79
8,12,48,52,68,84
8,18,36,52,68,84
8,28,44,50,64,80
9,11,27,49,71,87
9,11,49,69,71,75
9,15,17,43,77,87
9,15,29,31,51,89
9,17,43,63,69,77
9,23,33,37,75,83
9,23,37,51,63,83
9,25,33,35,69,85
9,27,29,31,33,89
10,11,49,50,57,60,70,71
10,12,16,20,26,52,86,88
10,12,24,48,50,60,70,84
10,12,26,34,50,60,70,86
10,12,48,50,54,60,70,72
10,13,47,50,51,60,70,73
10,14,20,46,48,52,56,88
10,14,46,48,50,60,70,74
10,15,21,27,50,60,70,87
10,15,21,50,57,60,70,81
10,15,25,35,50,60,70,85
10,15,50,51,57,60,63,70
10,16,20,22,24,56,82,88
10,16,20,52,56,58,62,84
10,16,26,40,42,62,76,82
10,16,42,44,50,60,70,76
10,17,39,43,50,60,70,77
10,18,24,36,50,60,70,84
10,18,36,42,50,60,70,78
10,19,33,41,50,60,70,79
10,21,23,37,50,60,70,83
10,21,27,39,50,60,70,81
10,22,24,38,50,60,70,82
10,26,40,46,52,62,66,68
10,27,33,39,50,60,70,75
1,10,50,59,60,61,70,87
11,12,24,48,49,57,71,84
11,12,26,34,49,57,71,86
11,12,48,49,54,57,71,72
11,13,25,27,47,49,53,89
11,13,27,47,49,71,73,75
11,13,47,49,51,57,71,73
11,14,46,48,49,57,71,74
1,11,49,57,59,61,71,87
11,15,17,25,49,53,57,89
11,15,21,27,49,57,71,87
11,15,25,35,49,57,71,85
11,15,31,35,57,67,71,77
11,16,42,44,49,57,71,76
11,17,25,27,39,49,53,89
11,17,25,35,39,61,77,83
11,17,39,43,49,57,71,77
11,18,24,36,49,57,71,84
11,18,36,42,49,57,71,78
11,20,30,40,49,57,71,80
11,21,23,37,49,57,71,83
11,21,27,39,49,57,71,81
11,22,24,38,49,57,71,82
1,12,24,48,59,61,84,87
1,12,26,34,59,61,86,87
1,12,48,54,59,61,72,87
11,25,27,35,39,49,71,85
11,25,35,47,53,61,67,69
11,27,31,35,39,67,71,77
11,27,31,35,47,67,71,73
1,13,47,51,59,61,73,87
1,13,47,59,61,73,75,81
1,14,46,48,59,61,74,87
1,15,21,57,59,61,81,87
1,15,25,35,59,61,85,87
1,15,35,41,61,67,77,87
1,15,51,57,59,61,63,87
1,16,42,44,59,61,76,87
1,17,39,43,59,61,77,87
1,18,24,36,59,61,84,87
1,18,36,42,59,61,78,87
1,19,33,41,59,61,79,87
1,19,41,59,61,63,79,81
1,20,30,40,59,61,80,87
1,21,23,37,59,61,83,87
1,21,27,37,65,71,73,87
1,21,27,39,59,61,81,87
12,13,24,47,48,51,73,84
12,13,26,34,47,51,73,86
12,13,47,48,51,54,72,73
1,21,37,41,65,73,79,81
1,21,37,57,65,71,73,81
12,14,26,34,46,48,74,86
12,15,21,24,27,48,84,87
12,15,21,24,48,57,81,84
12,15,21,26,27,34,86,87
12,15,21,26,34,57,81,86
12,15,21,27,48,54,72,87
12,15,21,48,54,57,72,81
12,15,24,25,35,48,84,85
12,15,24,48,51,57,63,84
12,15,25,26,34,35,85,86
12,15,25,35,48,54,72,85
12,15,26,34,51,57,63,86
12,15,48,51,54,57,63,72
12,16,24,28,32,44,76,88
12,16,26,34,42,44,76,86
12,17,24,39,43,48,77,84
12,17,26,34,39,43,77,86
12,17,39,43,48,54,72,77
12,18,24,26,34,36,84,86
12,19,24,33,41,48,79,84
12,19,26,33,34,41,79,86
12,19,33,41,48,54,72,79
12,20,24,30,40,48,80,84
12,20,26,30,34,40,80,86
12,20,30,40,48,54,72,80
12,21,23,24,37,48,83,84
12,21,23,26,34,37,83,86
12,21,23,37,48,54,72,83
12,21,24,27,39,48,81,84
12,21,26,27,34,39,81,86
12,21,27,39,48,54,72,81
12,22,24,26,34,38,82,86
12,22,24,38,48,54,72,82
1,22,24,38,59,61,82,87
12,24,27,33,39,48,75,84
12,26,27,33,34,39,75,86
12,26,32,34,40,68,70,76
12,27,33,39,48,54,72,75
1,23,37,43,59,63,79,85
1,23,37,59,61,63,75,83
1,25,35,39,59,61,81,85
1,25,35,59,61,63,69,85
1,2,58,59,61,62,84,87
1,27,33,39,59,61,75,87
13,14,46,47,48,51,73,74
13,15,19,25,47,51,53,89
13,15,21,27,47,51,73,87
13,15,21,47,51,57,73,81
13,15,25,35,47,51,73,85
13,16,42,44,47,51,73,76
13,18,24,36,47,51,73,84
13,18,36,42,47,51,73,78
13,19,21,23,55,59,79,81
13,19,23,25,33,59,79,85
13,19,23,33,55,59,75,79
13,19,23,51,55,59,63,79
13,19,25,27,33,47,53,89
13,19,25,47,53,59,61,81
13,19,33,41,47,51,73,79
13,20,30,40,47,51,73,80
13,21,23,27,29,49,55,89
13,21,23,27,49,55,59,87
13,21,23,37,47,51,73,83
13,21,23,49,55,57,59,81
13,22,24,38,47,51,73,82
13,23,49,51,55,57,59,63
13,25,27,33,35,47,73,85
1,33,35,37,41,73,79,85
1,33,37,41,65,73,75,79
1,35,37,39,43,71,77,85
1,35,37,41,61,63,77,83
1,35,39,41,61,67,77,81
1,35,41,47,61,67,73,81
1,35,41,61,63,67,69,77
1,37,39,43,65,71,75,77
1,37,41,43,63,65,77,79
1,37,41,51,63,65,73,79
1,37,43,57,63,65,71,77
1,37,51,57,63,65,71,73
14,15,21,27,46,48,74,87
14,15,21,46,48,57,74,81
14,15,25,35,46,48,74,85
14,15,46,48,51,57,63,74
14,17,39,43,46,48,74,77
14,18,24,36,46,48,74,84
14,18,26,34,36,46,74,86
14,19,33,41,46,48,74,79
14,20,22,50,56,58,64,78
14,20,30,40,46,48,74,80
14,21,23,37,46,48,74,83
14,21,27,39,46,48,74,81
14,22,24,38,46,48,74,82
14,27,33,39,46,48,74,75
1,4,56,59,61,64,78,87
15,16,21,27,42,44,76,87
15,16,21,42,44,57,76,81
15,16,25,35,42,44,76,85
15,16,42,44,51,57,63,76
15,17,19,21,23,25,83,89
15,17,19,25,53,59,61,87
15,17,19,41,43,63,77,79
15,17,21,27,39,43,77,87
15,17,21,39,43,57,77,81
15,17,25,35,39,43,77,85
15,18,21,24,27,36,84,87
15,18,21,24,36,57,81,84
15,18,21,27,36,42,78,87
15,18,21,36,42,57,78,81
15,18,24,25,35,36,84,85
15,18,24,36,51,57,63,84
15,18,25,35,36,42,78,85
15,18,36,42,51,57,63,78
15,19,21,27,33,41,79,87
15,19,25,33,35,41,79,85
15,20,21,27,30,40,80,87
15,20,21,30,40,57,80,81
15,20,25,30,35,40,80,85
15,20,30,40,51,57,63,80
15,21,22,24,27,38,82,87
15,21,22,24,38,57,81,82
15,21,23,25,35,37,83,85
15,21,23,29,37,43,79,85
15,21,23,37,51,57,63,83
15,21,25,27,35,39,81,85
15,21,31,35,37,41,77,83
15,22,24,25,35,38,82,85
15,22,24,38,51,57,63,82
15,31,35,41,47,51,67,73
1,5,41,61,65,67,77,87
1,5,55,59,61,65,75,87
16,17,39,42,43,44,76,77
16,18,24,36,42,44,76,84
16,19,33,41,42,44,76,79
16,20,22,42,44,50,58,86
16,20,30,40,42,44,76,80
16,21,23,37,42,44,76,83
16,21,27,39,42,44,76,81
16,22,24,38,42,44,76,82
16,27,33,39,42,44,75,76
1,6,28,32,59,61,87,88
1,6,42,59,61,66,78,87
1,6,54,59,61,66,72,87
1,7,13,59,73,79,81,85
1,7,15,43,59,79,85,87
17,18,24,36,39,43,77,84
17,18,36,39,42,43,77,78
17,19,23,25,59,61,63,83
17,19,23,43,55,59,63,79
17,19,25,27,33,39,53,89
17,19,25,39,53,59,61,81
17,19,25,53,59,61,63,69
17,19,33,39,41,43,77,79
17,20,30,39,40,43,77,80
17,21,23,37,39,43,77,83
17,22,24,38,39,43,77,82
17,23,25,39,43,49,59,85
17,23,39,43,49,55,59,75
17,23,43,49,55,57,59,63
1,7,27,65,67,71,73,87
1,7,35,67,69,71,73,85
1,7,39,43,59,79,81,85
1,7,41,65,67,73,79,81
1,7,43,55,59,65,79,87
1,7,43,59,63,69,79,85
1,7,53,59,61,67,69,87
1,7,57,65,67,71,73,81
1,7,65,67,69,71,73,75
18,19,24,33,36,41,79,84
18,19,33,36,41,42,78,79
18,20,24,30,36,40,80,84
18,20,30,36,40,42,78,80
18,21,23,24,36,37,83,84
18,21,23,36,37,42,78,83
18,21,24,27,36,39,81,84
18,21,27,36,39,42,78,81
18,22,24,36,38,42,78,82
18,24,27,33,36,39,75,84
18,27,33,36,39,42,75,78
1,8,52,59,61,66,68,87
19,20,30,33,40,41,79,80
19,21,23,33,37,41,79,83
19,21,27,33,39,41,79,81
19,22,24,33,38,41,79,82
19,25,33,35,41,47,61,83
1,9,33,59,61,69,75,87
1,9,37,43,65,71,77,87
1,9,37,51,65,71,73,87
1,9,51,59,61,63,69,87
20,21,23,30,37,40,80,83
20,21,27,30,39,40,80,81
20,22,24,30,38,40,80,82
20,27,30,33,39,40,75,80
2,10,50,58,60,62,70,84
2,11,49,57,58,62,71,84
21,22,23,24,37,38,82,83
21,22,24,27,38,39,81,82
2,12,26,34,58,62,84,86
21,23,27,33,37,39,75,83
21,23,29,37,43,55,65,79
2,12,48,54,58,62,72,84
21,27,29,31,37,65,71,73
2,13,47,51,58,62,73,84
2,14,46,48,58,62,74,84
2,14,46,58,62,66,74,78
2,15,21,27,58,62,84,87
2,15,21,57,58,62,81,84
2,15,25,35,58,62,84,85
2,15,51,57,58,62,63,84
2,16,42,44,58,62,76,84
2,17,39,43,58,62,77,84
2,18,36,42,58,62,78,84
2,19,33,41,58,62,79,84
2,20,30,40,58,62,80,84
2,21,23,37,58,62,83,84
2,21,27,39,58,62,81,84
2,22,24,38,58,62,82,84
2,22,38,42,58,62,78,82
2,22,38,54,58,62,72,82
22,24,27,33,38,39,75,82
22,24,28,38,44,50,64,80
2,26,34,42,58,62,66,86
2,27,33,39,58,62,75,84
2,3,29,31,58,62,84,89
2,3,39,58,62,75,81,84
2,34,38,42,44,70,76,80
2,3,57,58,62,63,81,84
2,3,58,62,63,69,75,84
2,4,38,64,70,74,78,80
2,4,40,62,68,70,76,84
2,4,56,58,62,64,78,84
2,5,55,58,62,65,75,84
27,31,33,35,39,41,67,77
27,31,33,35,41,47,67,73
2,7,53,58,62,67,69,84
2,8,34,66,68,70,74,80
2,8,44,50,58,64,80,84
2,8,52,58,62,66,68,84
2,9,15,51,58,62,84,87
2,9,27,33,58,62,84,87
2,9,33,58,62,69,75,84
2,9,51,58,62,63,69,84
3,10,29,31,50,60,70,89
3,10,39,50,60,70,75,81
3,10,50,57,60,63,70,81
3,10,50,60,63,69,70,75
3,11,25,31,35,47,83,89
3,11,29,31,49,57,71,89
3,11,39,49,57,71,75,81
3,11,49,57,63,69,71,75
3,12,24,29,31,48,84,89
3,12,24,39,48,75,81,84
3,12,24,48,57,63,81,84
3,12,24,48,63,69,75,84
3,12,26,29,31,34,86,89
3,12,26,34,39,75,81,86
3,12,26,34,57,63,81,86
3,12,26,34,63,69,75,86
3,12,29,31,48,54,72,89
3,12,39,48,54,72,75,81
3,12,48,54,57,63,72,81
3,12,48,54,63,69,72,75
3,13,19,25,47,53,81,89
3,13,23,25,29,49,85,89
3,13,23,29,49,55,75,89
3,13,25,35,47,73,81,85
3,13,29,31,47,51,73,89
3,13,47,51,57,63,73,81
3,13,47,51,63,69,73,75
3,14,29,31,46,48,74,89
3,14,39,46,48,74,75,81
3,14,46,48,57,63,74,81
3,14,46,48,63,69,74,75
3,15,21,29,31,57,81,89
3,15,25,29,31,35,85,89
3,15,25,35,57,63,81,85
3,15,29,31,51,57,63,89
3,16,29,31,42,44,76,89
3,16,39,42,44,75,76,81
3,16,42,44,57,63,76,81
3,16,42,44,63,69,75,76
3,17,19,23,25,63,83,89
3,17,19,25,39,53,81,89
3,17,19,25,53,63,69,89
3,17,29,31,39,43,77,89
3,17,39,43,57,63,77,81
3,17,39,43,63,69,75,77
3,18,24,29,31,36,84,89
3,18,24,36,39,75,81,84
3,18,24,36,57,63,81,84
3,18,24,36,63,69,75,84
3,18,29,31,36,42,78,89
3,18,36,39,42,75,78,81
3,18,36,42,57,63,78,81
3,18,36,42,63,69,75,78
3,19,29,31,33,41,79,89
3,19,33,39,41,75,79,81
3,19,33,41,63,69,75,79
3,20,29,30,31,40,80,89
3,20,30,39,40,75,80,81
3,20,30,40,57,63,80,81
3,20,30,40,63,69,75,80
3,21,23,29,31,37,83,89
3,21,23,37,39,75,81,83
3,21,23,37,57,63,81,83
3,21,27,29,31,39,81,89
3,22,24,29,31,38,82,89
3,22,24,38,39,75,81,82
3,22,24,38,57,63,81,82
3,22,24,38,63,69,75,82
3,23,25,35,37,63,83,85
3,23,29,37,43,63,79,85
3,25,33,35,39,69,75,85
3,27,29,31,33,39,75,89
3,29,31,35,37,71,73,85
3,29,31,37,65,71,73,75
3,31,35,37,41,63,77,83
3,31,35,39,41,67,77,81
3,31,35,41,47,67,73,81
3,31,35,41,63,67,69,77
3,4,29,31,56,64,78,89
3,4,39,56,64,75,78,81
3,4,56,57,63,64,78,81
3,4,56,63,64,69,75,78
3,5,11,31,47,75,83,89
3,5,29,31,55,65,75,89
3,5,55,57,63,65,75,81
3,6,28,29,31,32,88,89
3,6,28,32,39,75,81,88
3,6,28,32,57,63,81,88
3,6,28,32,63,69,75,88
3,6,29,31,42,66,78,89
3,6,29,31,54,66,72,89
3,6,39,42,66,75,78,81
3,6,39,54,66,72,75,81
3,6,42,57,63,66,78,81
3,6,42,63,66,69,75,78
3,6,54,57,63,66,72,81
3,6,54,63,66,69,72,75
3,7,13,29,73,79,81,85
3,7,29,31,53,67,69,89
3,7,29,39,43,79,81,85
3,7,29,43,63,69,79,85
3,7,39,53,67,69,75,81
3,7,53,57,63,67,69,81
3,8,29,31,52,66,68,89
3,8,39,52,66,68,75,81
3,8,52,57,63,66,68,81
3,8,52,63,66,68,69,75
3,9,29,31,33,69,75,89
3,9,29,31,51,63,69,89
4,10,40,46,56,62,78,82
4,10,50,56,60,64,70,78
4,11,49,56,57,64,71,78
4,13,47,51,56,64,73,78
4,14,46,48,56,64,74,78
4,15,21,27,56,64,78,87
4,15,21,56,57,64,78,81
4,15,25,35,56,64,78,85
4,15,51,56,57,63,64,78
4,16,24,44,56,64,76,84
4,16,42,44,56,64,76,78
4,16,44,54,56,64,72,76
4,17,39,43,56,64,77,78
4,18,24,36,56,64,78,84
4,19,33,41,56,64,78,79
4,20,30,40,56,64,78,80
4,21,23,37,56,64,78,83
4,21,27,39,56,64,78,81
4,22,24,38,56,64,78,82
4,24,28,32,48,56,64,88
4,24,32,38,40,70,76,82
4,27,33,39,56,64,75,78
4,32,40,46,48,68,70,74
4,5,55,56,64,65,75,78
4,6,28,32,56,64,78,88
4,6,54,56,64,66,72,78
4,7,53,56,64,67,69,78
4,8,48,52,56,64,68,84
4,8,52,56,64,66,68,78
4,9,15,51,56,64,78,87
4,9,27,33,56,64,78,87
4,9,33,56,64,69,75,78
4,9,51,56,63,64,69,78
5,10,50,55,60,65,70,75
5,11,17,39,61,75,77,83
5,11,17,49,53,55,57,89
5,11,17,57,61,63,77,83
5,11,21,27,31,47,83,89
5,11,21,27,47,61,83,87
5,11,21,47,57,61,81,83
5,11,27,31,47,53,67,89
5,11,27,47,53,61,67,87
5,11,31,57,65,67,71,77
5,11,47,51,57,61,63,83
5,11,47,53,57,61,67,81
5,11,47,53,61,67,69,75
5,11,49,55,57,65,71,75
5,12,24,48,55,65,75,84
5,12,26,34,55,65,75,86
5,12,48,54,55,65,72,75
5,13,19,47,51,53,55,89
5,13,47,51,55,65,73,75
5,14,46,48,55,65,74,75
5,15,21,51,55,57,65,87
5,16,42,44,55,65,75,76
5,17,19,21,23,55,83,89
5,17,19,41,61,63,77,83
5,17,19,53,55,59,61,87
5,17,39,43,55,65,75,77
5,17,43,55,57,63,65,77
5,18,24,36,55,65,75,84
5,18,36,42,55,65,75,78
5,19,21,41,47,61,81,83
5,19,21,41,55,65,79,81
5,19,33,41,47,61,75,83
5,19,33,41,55,65,75,79
5,19,41,47,51,61,63,83
5,19,41,47,53,61,67,81
5,19,41,51,55,63,65,79
5,20,30,40,55,65,75,80
5,21,23,37,55,65,75,83
5,21,27,29,31,55,65,89
5,21,27,39,55,65,75,81
5,21,31,37,41,65,77,83
5,22,24,38,55,65,75,82
5,31,41,47,51,65,67,73
5,6,28,32,55,65,75,88
5,6,42,55,65,66,75,78
5,6,54,55,65,66,72,75
5,7,27,53,55,65,67,87
5,7,53,55,57,65,67,81
5,7,53,55,65,67,69,75
5,8,52,55,65,66,68,75
5,9,11,17,31,77,83,89
5,9,11,17,61,77,83,87
5,9,11,31,47,51,83,89
5,9,11,47,51,61,83,87
5,9,17,43,55,65,77,87
5,9,27,33,55,65,75,87
5,9,29,31,51,55,65,89
5,9,51,55,63,65,69,75
6,10,26,32,40,46,82,88
6,10,28,32,50,60,70,88
6,10,42,50,60,66,70,78
6,10,50,54,60,66,70,72
6,11,28,32,49,57,71,88
6,11,42,49,57,66,71,78
6,11,49,54,57,66,71,72
6,12,26,28,32,34,86,88
6,12,26,34,54,66,72,86
6,12,28,32,48,54,72,88
6,13,28,32,47,51,73,88
6,13,42,47,51,66,73,78
6,13,47,51,54,66,72,73
6,14,20,22,28,50,86,88
6,14,22,38,46,74,78,82
6,14,26,34,46,66,74,86
6,14,28,32,46,48,74,88
6,14,46,48,54,66,72,74
6,15,21,27,28,32,87,88
6,15,21,27,42,66,78,87
6,15,21,27,54,66,72,87
6,15,21,28,32,57,81,88
6,15,21,42,57,66,78,81
6,15,21,54,57,66,72,81
6,15,25,28,32,35,85,88
6,15,25,35,42,66,78,85
6,15,25,35,54,66,72,85
6,15,28,32,51,57,63,88
6,15,42,51,57,63,66,78
6,15,51,54,57,63,66,72
6,16,28,32,42,44,76,88
6,16,42,44,54,66,72,76
6,17,28,32,39,43,77,88
6,17,39,42,43,66,77,78
6,17,39,43,54,66,72,77
6,18,28,32,36,42,78,88
6,19,28,32,33,41,79,88
6,19,33,41,42,66,78,79
6,19,33,41,54,66,72,79
6,20,28,30,32,40,80,88
6,20,30,40,42,66,78,80
6,20,30,40,54,66,72,80
6,21,23,28,32,37,83,88
6,21,23,37,42,66,78,83
6,21,23,37,54,66,72,83
6,21,27,28,32,39,81,88
6,21,27,39,42,66,78,81
6,21,27,39,54,66,72,81
6,22,24,28,32,38,82,88
6,22,26,34,38,42,82,86
6,27,28,32,33,39,75,88
6,27,33,39,42,66,75,78
6,27,33,39,54,66,72,75
6,28,32,34,38,70,74,80
6,7,28,32,53,67,69,88
6,7,42,53,66,67,69,78
6,7,53,54,66,67,69,72
6,8,28,32,52,66,68,88
6,9,15,28,32,51,87,88
6,9,15,42,51,66,78,87
6,9,15,51,54,66,72,87
6,9,27,28,32,33,87,88
6,9,27,33,42,66,78,87
6,9,27,33,54,66,72,87
6,9,28,32,33,69,75,88
6,9,28,32,51,63,69,88
6,9,33,42,66,69,75,78
6,9,33,54,66,69,72,75
6,9,42,51,63,66,69,78
6,9,51,54,63,66,69,72
7,10,50,53,60,67,69,70
7,11,49,53,57,67,69,71
7,12,24,48,53,67,69,84
7,12,26,34,53,67,69,86
7,12,48,53,54,67,69,72
7,13,15,29,51,73,79,85
7,13,19,53,55,59,79,81
7,13,25,49,53,59,69,85
7,13,27,29,33,73,79,85
7,13,27,29,49,53,55,89
7,13,27,29,49,71,73,85
7,13,27,47,53,67,73,81
7,13,27,49,53,55,59,87
7,13,29,51,55,65,73,79
7,13,47,51,53,67,69,73
7,13,49,53,55,57,59,81
7,13,49,53,55,59,69,75
7,14,46,48,53,67,69,74
7,15,19,41,53,67,79,81
7,15,25,35,53,67,69,85
7,15,27,29,31,53,67,89
7,15,29,43,49,57,71,85
7,15,51,53,57,63,67,69
7,16,42,44,53,67,69,76
7,17,39,43,53,67,69,77
7,18,24,36,53,67,69,84
7,18,36,42,53,67,69,78
7,19,33,41,53,67,69,79
7,20,30,40,53,67,69,80
7,22,24,38,53,67,69,82
7,27,29,31,65,67,71,73
7,27,29,33,39,43,79,85
7,27,29,39,43,49,71,85
7,27,33,39,53,67,69,75
7,29,43,49,55,57,65,71
7,8,52,53,66,67,68,69
7,9,15,51,53,67,69,87
7,9,27,33,53,67,69,87
7,9,29,33,43,69,79,85
7,9,29,43,49,69,71,85
8,10,50,52,60,66,68,70
8,11,49,52,57,66,68,71
8,12,16,44,52,68,76,84
8,12,26,34,52,66,68,86
8,12,28,32,48,52,68,88
8,12,28,34,44,50,80,86
8,12,48,52,54,66,68,72
8,13,47,51,52,66,68,73
8,14,20,50,52,58,66,86
8,14,28,48,50,64,74,80
8,14,46,48,52,66,68,74
8,15,21,27,52,66,68,87
8,15,21,52,57,66,68,81
8,15,25,35,52,66,68,85
8,15,51,52,57,63,66,68
8,16,42,44,52,66,68,76
8,17,39,43,52,66,68,77
8,18,28,32,36,52,68,88
8,18,36,42,52,66,68,78
8,19,33,41,52,66,68,79
8,20,30,40,52,66,68,80
8,21,23,37,52,66,68,83
8,21,27,39,52,66,68,81
8,27,33,39,52,66,68,75
8,9,15,51,52,66,68,87
8,9,27,33,52,66,68,87
8,9,33,52,66,68,69,75
8,9,51,52,63,66,68,69
9,10,15,50,51,60,70,87
9,10,27,33,50,60,70,87
9,10,33,50,60,69,70,75
9,10,50,51,60,63,69,70
9,11,15,49,51,57,71,87
9,11,17,23,25,49,83,89
9,11,17,25,49,53,69,89
9,11,23,37,49,71,75,83
9,11,25,35,49,69,71,85
9,11,27,29,31,49,71,89
9,11,31,35,37,71,77,83
9,11,31,35,67,69,71,77
9,11,49,51,57,63,69,71
9,12,15,24,48,51,84,87
9,12,15,26,34,51,86,87
9,12,15,48,51,54,72,87
9,12,24,27,33,48,84,87
9,12,24,33,48,69,75,84
9,12,24,48,51,63,69,84
9,12,26,27,33,34,86,87
9,12,26,33,34,69,75,86
9,12,26,34,51,63,69,86
9,12,27,33,48,54,72,87
9,12,33,48,54,69,72,75
9,12,48,51,54,63,69,72
9,13,23,29,49,51,55,89
9,13,23,49,51,55,59,87
9,13,27,33,47,51,73,87
9,13,33,47,51,69,73,75
9,14,15,46,48,51,74,87
9,14,27,33,46,48,74,87
9,14,33,46,48,69,74,75
9,14,46,48,51,63,69,74
9,15,16,42,44,51,76,87
9,15,17,29,31,43,77,89
9,15,18,24,36,51,84,87
9,15,18,36,42,51,78,87
9,15,19,33,41,51,79,87
9,15,20,30,40,51,80,87
9,15,21,23,37,51,83,87
9,15,22,24,38,51,82,87
9,15,25,27,33,35,85,87
9,15,25,35,51,63,69,85
9,16,27,33,42,44,76,87
9,16,33,42,44,69,75,76
9,16,42,44,51,63,69,76
9,17,19,23,25,33,83,89
9,17,19,25,33,53,69,89
9,17,23,29,43,49,55,89
9,17,23,37,43,63,77,83
9,17,23,43,49,55,59,87
9,17,27,33,39,43,77,87
9,17,33,39,43,69,75,77
9,18,24,27,33,36,84,87
9,18,24,33,36,69,75,84
9,18,24,36,51,63,69,84
9,18,27,33,36,42,78,87
9,18,33,36,42,69,75,78
9,18,36,42,51,63,69,78
9,19,33,41,51,63,69,79
9,20,27,30,33,40,80,87
9,20,30,33,40,69,75,80
9,20,30,40,51,63,69,80
9,21,23,27,33,37,83,87
9,22,24,27,33,38,82,87
9,22,24,33,38,69,75,82
9,22,24,38,51,63,69,82
9,23,25,33,35,37,83,85
9,23,29,33,37,43,79,85
9,23,29,37,43,49,71,85
9,29,31,37,43,65,71,77
9,29,31,37,51,65,71,73
9,31,33,35,37,41,77,83
9,31,33,35,41,67,69,77
谢谢mathe!有这33个解, 6项与4项的关系就清晰了。
: {01, 35, 37, 71, 73, 85},
: {01, 37, 65, 71, 73, 75},
: {01, 39, 59, 61, 75, 81},
: {01, 57, 59, 61, 63, 81},
: {01, 59, 61, 63, 69, 75},
: {02, 34, 38, 70, 74, 80},
: {02, 42, 58, 62, 66, 78},
: {02, 54, 58, 62, 66, 72},
: {03, 13, 47, 73, 75, 81},
: {03, 19, 41, 63, 79, 81},
: {03, 23, 37, 63, 75, 83},
: {03, 25, 35, 39, 81, 85},
: {03, 25, 35, 63, 69, 85},
: {04, 24, 48, 56, 64, 84},
: {04, 32, 40, 68, 70, 76},
: {04, 48, 54, 56, 64, 72},
: {05, 11, 47, 61, 75, 83},
: {05, 21, 55, 57, 65, 81},
: {05, 31, 41, 65, 67, 77},
: {05, 51, 55, 57, 63, 65},
: {06, 14, 46, 66, 74, 78},
: {06, 22, 38, 42, 78, 82},
: {06, 22, 38, 54, 72, 82},
: {07, 15, 53, 57, 67, 81},
: {07, 27, 39, 53, 67, 81},
: {07, 29, 43, 55, 65, 79},
: {08, 28, 44, 50, 64, 80},
: {09, 11, 49, 69, 71, 75},
: {09, 17, 43, 63, 69, 77},
: {11, 27, 39, 49, 71, 75},
: {12, 16, 44, 54, 72, 76},
: {13, 23, 49, 55, 59, 75},
: {13, 27, 33, 47, 73, 75},
计算机计算表示，只有下面这些是基础解
1, 59, 61, 87,
2, 58, 62, 84,
3, 63, 69, 75,
3, 57, 63, 81,
4, 56, 64, 78,
5, 55, 65, 75,
6, 54, 66, 72,
7, 53, 67, 69,
8, 52, 66, 68,
9, 51, 63, 69,
10, 50, 60, 70,
11, 49, 57, 71,
12, 48, 54, 72,
13, 47, 51, 73,
14, 46, 48, 74,
15, 51, 57, 63,
9, 15, 51, 87,
15, 21, 57, 81,
12, 24, 48, 84,
5, 11, 47, 61, 75, 83,
5, 17, 19, 53, 55, 89,
10, 16, 20, 52, 56, 88,
14, 20, 22, 50, 58, 86,
13, 23, 49, 55, 59, 75,
15, 17, 19, 25, 53, 89,
13, 23, 25, 49, 59, 85,
11, 25, 35, 47, 61, 83,
10, 26, 40, 46, 62, 82,
1, 7, 13, 59, 73, 79, 81, 85,
7, 13, 19, 53, 55, 59, 79, 81,
13, 19, 25, 47, 53, 59, 61, 81,
9, 11, 17, 23, 25, 49, 83, 89,
17, 19, 23, 25, 59, 61, 63, 83,
11, 13, 25, 27, 47, 49, 53, 89,
7, 13, 27, 29, 49, 71, 73, 85,
7, 13, 27, 29, 49, 53, 55, 89,
5, 11, 27, 31, 47, 53, 67, 89,
11, 27, 31, 35, 47, 67, 71, 73,
5, 19, 41, 47, 53, 61, 67, 81,
1, 35, 41, 47, 61, 67, 73, 81,
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
11, 25, 35, 47, 61, 83,
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
11, 25, 35, 47, 61, 83, 80, 64, 50, 28, 8
又比如
3, 63, 69, 75,
3, 57, 63, 81,
有公共元，可以消除它们公共元并拼接成
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。
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。
=05, 17, 19, 53, 55, 89,
=15, 17, 19, 25, 53, 89,
=05, 55, 65, 75,
比较,=比较,,由可知=。
=05, 11, 47, 61, 75, 83,
=11, 25, 35, 47, 61, 83,
=05, 55, 65, 75,
比较,=比较,,由可知=。
=13, 23, 49, 55, 59, 75,
=13, 23, 25, 49, 59, 85,
=05, 55, 65, 75,
比较,=比较,,由可知=。
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。
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,