单位分数 42项解

问题见：

http://www.mysanco.com/index.php?class=wenku&action=wenku_item&id=11&type=wb

程序找到的解：

17,19,20,21,22,24,26,27,30,32,33,34,35,36,39,40,42,44,48,50,52,54,55,56,57,60,63,66,70,72,75,76,77,78,80,84,85,88,90,91,96,99
17,18,19,21,22,24,26,27,30,32,33,34,35,39,40,42,44,45,48,50,52,54,55,56,57,60,63,66,70,72,75,76,77,78,80,84,85,88,90,91,96,99
14,17,21,22,24,26,27,28,30,32,33,34,35,36,38,39,40,44,48,50,52,54,55,56,60,63,66,70,72,75,76,77,78,80,84,85,88,90,91,95,96,99
12,17,21,22,24,26,27,30,32,33,34,35,36,38,39,40,42,44,48,50,52,54,55,56,60,63,66,70,72,75,76,77,78,80,84,85,88,90,91,95,96,99
17,18,19,22,24,26,27,28,30,32,33,34,35,36,39,40,42,44,45,48,50,52,54,55,56,57,60,66,70,72,75,76,77,78,80,84,85,88,90,91,96,99
17,18,20,21,22,24,26,27,28,30,32,33,34,38,39,40,44,45,48,50,52,54,55,56,60,63,66,70,72,75,76,77,78,80,84,85,88,90,91,95,96,99
17,18,20,21,22,24,26,27,30,32,33,34,35,38,39,40,42,44,45,48,50,52,54,55,56,63,66,70,72,75,76,77,78,80,84,85,88,90,91,95,96,99
17,18,20,21,22,24,26,27,30,32,33,34,36,38,39,40,42,44,45,48,50,52,54,55,56,60,66,70,72,75,76,77,78,80,84,85,88,90,91,95,96,99
15,17,18,21,22,24,26,27,32,33,34,35,38,39,40,42,44,45,48,50,52,54,55,56,60,63,66,70,72,75,76,77,78,80,84,85,88,90,91,95,96,99
13,17,18,21,22,24,26,27,32,33,34,35,38,40,42,44,45,48,50,52,54,55,56,60,63,65,66,70,72,75,76,77,78,80,84,85,88,90,91,95,96,99
15,17,20,21,22,24,26,27,32,33,34,35,36,38,39,40,42,44,48,50,52,54,55,56,60,63,66,70,72,75,76,77,78,80,84,85,88,90,91,95,96,99
17,18,20,21,22,24,26,27,32,33,34,35,36,38,39,40,42,44,45,48,50,52,54,55,56,60,63,66,70,72,75,76,77,78,80,84,85,88,91,95,96,99
15,17,20,21,22,24,26,30,32,33,34,35,36,38,39,40,42,44,45,48,50,52,55,56,60,63,66,70,72,75,76,77,78,80,84,85,88,90,91,95,96,99
15,17,20,21,22,26,27,30,32,33,34,35,36,38,39,40,42,44,45,48,50,52,54,55,56,60,63,66,70,75,76,77,78,80,84,85,88,90,91,95,96,99
13,17,20,21,22,24,26,27,32,33,34,35,36,38,40,42,44,48,50,52,54,55,56,60,63,65,66,70,72,75,76,77,78,80,84,85,88,90,91,95,96,99
17,18,21,22,24,26,27,28,30,32,33,34,35,36,38,39,40,42,44,45,48,50,52,54,55,56,60,66,72,75,76,77,78,80,84,85,88,90,91,95,96,99
17,18,20,22,24,26,27,28,30,32,33,34,35,36,38,39,40,42,44,45,48,50,52,54,55,56,66,70,72,75,76,77,78,80,84,85,88,90,91,95,96,99
15,17,18,22,24,26,27,28,32,33,34,35,36,38,39,40,42,44,45,48,50,52,54,55,56,60,66,70,72,75,76,77,78,80,84,85,88,90,91,95,96,99
13,17,18,22,24,26,27,28,32,33,34,35,36,38,40,42,44,45,48,50,52,54,55,56,60,65,66,70,72,75,76,77,78,80,84,85,88,90,91,95,96,99
15,17,20,21,24,26,27,30,32,33,34,35,36,38,39,40,42,44,45,48,50,52,54,55,56,60,63,66,70,72,75,76,77,78,80,84,85,88,90,91,95,96
13,17,20,21,24,26,27,30,32,33,34,35,36,38,40,42,44,45,48,50,52,54,55,56,60,63,65,66,70,72,75,76,77,78,80,84,85,88,90,91,95,96
13,17,20,21,22,24,26,30,32,33,34,35,36,38,40,42,44,45,48,50,52,55,56,60,63,65,66,70,72,75,76,77,78,80,84,85,88,90,91,95,96,99
13,17,20,21,22,26,27,30,32,33,34,35,36,38,40,42,44,45,48,50,52,54,55,56,60,63,65,66,70,75,76,77,78,80,84,85,88,90,91,95,96,99
15,17,20,22,24,26,27,28,30,32,33,34,35,38,39,40,42,44,45,48,50,52,54,55,56,60,66,70,72,75,76,77,78,80,84,85,88,90,91,95,96,99
13,17,20,22,24,26,27,28,30,32,33,34,35,38,40,42,44,45,48,50,52,54,55,56,60,65,66,70,72,75,76,77,78,80,84,85,88,90,91,95,96,99

　　

 另找到：

17,18,20,21,22,24,26,27,30,32,33,34,35,38,39,40,42,44,45,48,50,54,55,56,60,63,65,66,70,72,75,76,77,80,84,85,88,90,91,95,96,99
17,18,20,22,24,26,27,28,30,32,33,34,35,36,38,39,40,42,44,45,48,50,54,55,56,60,65,66,70,72,75,76,77,80,84,85,88,90,91,95,96,99

　　

与

15,17,20,21,22,26,27,30,32,33,34,35,36,38,39,40,42,44,45,48,50,52,54,55,56,60,63,66,70,75,76,77,78,80,84,85,88,90,91,95,96,99

　　

 相比：

1/19+1/24+1/57+1/72=1/15+1/38+1/45+1/95
1/18+1/19+1/24+1/57+1/72=1/15+1/20+1/36+1/38+1/95
1/14+1/24+1/28+1/72=1/15+1/20+1/42+1/45
1/12+1/24+1/72=1/15+1/20+1/45
1/18+1/19+1/24+1/28+1/57+1/72=1/15+1/20+1/21+1/38+1/63+1/95
1/18+1/24+1/28+1/72=1/15+1/35+1/36+1/42
1/18+1/24+1/72=1/15+1/36+1/60
1/18+1/24+1/72=1/15+1/35+1/63
1/18+1/24+1/72=1/20+1/30+1/36
1/13+1/18+1/24+1/65+1/72=1/15+1/20+1/30+1/36+1/39
1/24+1/72=1/30+1/45
1/18+1/24+1/72=1/15+1/30+1/90
1/24+1/72=1/27+1/54
 ==
1/13+1/24+1/65+1/72=1/15+1/30+1/39+1/45
1/18+1/24+1/28+1/72=1/15+1/20+1/63+1/70
1/18+1/24+1/28+1/72=1/15+1/21+1/60+1/63
1/18+1/24+1/28+1/72=1/20+1/21+1/30+1/63
1/13+1/18+1/24+1/28+1/65+1/72=1/15+1/20+1/21+1/30+1/39+1/63
1/24+1/72=1/22+1/99
1/13+1/24+1/65+1/72=1/15+1/22+1/39+1/99
1/13+1/24+1/65+1/72=1/15+1/27+1/39+1/54
1/13+1/65=1/15+1/39
1/24+1/28+1/72=1/21+1/36+1/63
1/13+1/24+1/28+1/65+1/72=1/15+1/21+1/36+1/39+1/63

　　

1/18+1/24+1/65+1/72=1/15+1/36+1/52+1/78
1/18+1/24+1/28+1/65+1/72=1/15+1/21+1/52+1/63+1/78