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从1到100这100个自然数中任取10个数，使他们的倒数和等于1。这10个数分别是多少？

news 来源：原创 2024/4/28 1:35:33

用枚举法得到了所有答案（69014条），还耗了很多电。

程序：15线程。
cpu：i7-9700。
耗时：1217分钟（20小时17分钟）。

链接: 所有答案
提取码：rwf5

这是一篇非常没有技术含量的文章。

特地为这个问题写一篇文章，并不是有什么重大发现，仅仅是分享一下结果。

话是十来分钟写的枚举算法，慢到令人摸不着头脑。第一天晚上开始执行，第三天下班回家看到了运行结果，真是漫长啊~~

贴部分结果，给做题学生的家长取用：

结果
2,3,14,55,60,70,77,84,90,99
2,3,14,55,63,70,77,78,91,99
2,3,14,56,60,66,77,88,90,99
2,3,14,56,60,72,78,84,90,91
2,3,14,56,63,66,77,84,88,99
2,3,15,38,70,76,78,84,91,95
2,3,15,40,66,70,77,88,90,99
2,3,15,40,70,72,78,84,90,91
2,3,15,42,55,77,78,90,91,99
2,3,15,45,60,70,78,84,90,91
2,3,15,45,66,70,72,77,88,99
2,3,15,48,55,70,77,80,90,99
2,3,15,48,56,72,78,80,90,91
2,3,15,48,60,70,78,80,84,91
2,3,15,50,55,70,75,77,90,99
2,3,15,50,56,72,75,78,90,91
2,3,15,50,60,70,75,78,84,91
2,3,15,55,56,63,72,77,90,99
2,3,15,55,56,66,72,78,90,91
2,3,15,55,60,63,70,77,84,99
2,3,15,55,60,66,70,78,84,91
2,3,15,56,60,63,66,77,88,99
2,3,15,56,60,63,72,78,84,91
2,3,16,32,70,78,80,84,91,96
2,3,16,33,70,78,80,84,88,91
2,3,16,35,70,72,78,80,90,91
2,3,16,36,66,70,77,80,88,99
2,3,16,36,70,72,78,80,84,91
2,3,16,38,56,76,78,80,91,95
2,3,16,38,60,72,76,80,90,95
2,3,16,38,63,72,76,80,84,95
2,3,16,40,55,70,77,80,90,99
2,3,16,40,56,72,78,80,90,91
2,3,16,40,60,70,78,80,84,91
2,3,16,42,56,70,78,80,84,91
2,3,16,42,60,70,72,80,84,90
2,3,16,42,63,70,72,78,80,91
2,3,16,44,56,70,77,78,80,91
2,3,16,44,60,70,72,77,80,90
2,3,16,44,63,70,72,77,80,84
2,3,16,45,48,70,78,84,90,91
2,3,16,45,55,70,72,77,80,99
2,3,16,45,56,60,78,80,90,91
2,3,16,45,56,63,78,80,84,91
2,3,16,45,60,63,72,80,84,90
2,3,16,48,50,70,75,78,84,91
2,3,16,48,55,60,70,77,90,99
2,3,16,48,55,63,70,77,84,99
2,3,16,48,55,66,70,78,84,91
2,3,16,48,56,60,72,78,90,91
2,3,16,48,56,63,66,77,88,99
2,3,16,48,56,63,72,78,84,91
2,3,16,50,55,66,72,75,80,90
2,3,16,50,56,60,75,78,80,91
2,3,16,50,60,63,72,75,80,84
2,3,16,55,56,60,63,77,80,99
2,3,16,55,56,60,66,78,80,91
2,3,16,55,60,63,66,72,80,84
2,3,17,34,55,70,77,85,90,99
2,3,17,34,56,72,78,85,90,91
2,3,17,34,60,70,78,84,85,91
2,3,18,25,70,78,84,90,91,100
2,3,18,28,66,72,77,84,88,99
2,3,18,30,60,70,78,84,90,91
2,3,18,30,66,70,72,77,88,99
2,3,18,32,55,70,72,77,96,99
2,3,18,32,56,60,78,90,91,96
2,3,18,32,56,63,78,84,91,96
2,3,18,32,60,63,72,84,90,96
2,3,18,33,55,70,72,77,88,99
2,3,18,33,56,60,78,88,90,91
2,3,18,33,56,63,78,84,88,91
2,3,18,33,56,66,72,78,91,99
2,3,18,33,60,63,66,84,90,99
2,3,18,33,60,63,72,84,88,90
2,3,18,35,44,77,78,84,90,91
2,3,18,35,48,70,78,80,90,91
2,3,18,35,50,70,75,78,90,91
2,3,18,35,55,63,70,77,90,99
2,3,18,35,55,66,70,78,90,91
2,3,18,35,56,63,72,78,90,91
2,3,18,35,60,63,70,78,84,91
2,3,18,36,45,70,78,84,90,91
2,3,18,36,48,70,78,80,84,91
2,3,18,36,50,70,75,78,84,91
2,3,18,36,55,60,70,77,90,99
2,3,18,36,55,63,70,77,84,99
2,3,18,36,55,66,70,78,84,91
2,3,18,36,56,60,72,78,90,91
2,3,18,36,56,63,66,77,88,99
2,3,18,36,56,63,72,78,84,91
2,3,18,38,42,70,76,84,90,95
2,3,18,38,44,70,76,77,90,95
2,3,18,38,45,63,76,84,90,95
2,3,18,38,48,60,76,80,90,95
2,3,18,38,48,63,76,80,84,95
2,3,18,38,50,60,75,76,90,95
2,3,18,38,50,63,75,76,84,95
2,3,18,38,55,60,66,76,90,95
2,3,18,38,55,63,66,76,84,95
2,3,18,40,45,66,70,77,88,99
2,3,18,40,45,70,72,78,84,91
2,3,18,40,48,56,78,80,90,91
2,3,18,40,48,63,72,80,84,90
2,3,18,40,50,56,75,78,90,91
2,3,18,40,50,63,72,75,84,90
2,3,18,40,55,56,63,77,90,99
2,3,18,40,55,56,66,78,90,91
2,3,18,40,55,60,70,72,77,99
2,3,18,40,55,63,66,72,84,90
2,3,18,40,56,60,63,78,84,91
2,3,18,42,44,60,77,78,90,91
2,3,18,42,44,63,77,78,84,91
2,3,18,42,45,55,77,78,91,99
2,3,18,42,45,63,70,78,90,91
2,3,18,42,48,60,70,80,84,90
2,3,18,42,48,63,70,78,80,91
2,3,18,42,50,60,70,75,84,90
2,3,18,42,50,63,70,75,78,91
2,3,18,42,55,56,70,72,77,99
2,3,18,42,55,60,66,70,84,90
2,3,18,42,55,63,66,70,78,91
2,3,18,42,56,60,63,72,84,90
2,3,18,44,45,63,70,77,84,90
2,3,18,44,48,60,70,77,80,90
2,3,18,44,48,63,70,77,80,84
2,3,18,44,50,60,70,75,77,90
2,3,18,44,50,63,70,75,77,84
2,3,18,44,55,60,66,70,77,90
2,3,18,44,55,63,66,70,77,84
2,3,18,44,56,60,63,72,77,90
2,3,18,45,48,55,70,77,80,99
2,3,18,45,48,56,72,78,80,91
2,3,18,45,48,60,63,80,84,90
2,3,18,45,50,55,70,75,77,99
2,3,18,45,50,56,72,75,78,91
2,3,18,45,50,60,63,75,84,90
2,3,18,45,55,56,63,72,77,99
2,3,18,45,55,56,66,72,78,91
2,3,18,45,55,60,63,66,84,90
2,3,18,48,50,55,66,75,80,90
2,3,18,48,50,60,63,75,80,84
2,3,18,48,55,60,63,66,80,84
2,3,18,50,55,60,63,66,75,84
2,3,19,30,57,70,76,78,84,91
2,3,19,32,56,57,76,78,91,96
2,3,19,32,57,60,72,76,90,96
2,3,19,32,57,63,72,76,84,96
2,3,19,33,56,57,76,78,88,91
2,3,19,33,57,60,66,76,90,99
2,3,19,33,57,60,72,76,88,90
2,3,19,33,57,63,66,76,84,99
2,3,19,33,57,63,72,76,84,88
2,3,19,35,56,57,72,76,84,90
2,3,19,35,57,60,70,76,78,91
2,3,19,36,55,57,70,76,77,99
2,3,19,36,56,57,72,76,78,91
2,3,19,36,57,60,63,76,84,90
2,3,19,40,48,57,72,76,80,90
2,3,19,40,50,57,72,75,76,90
2,3,19,40,55,57,66,72,76,90
2,3,19,40,56,57,60,76,78,91
2,3,19,40,57,60,63,72,76,84
2,3,19,42,44,57,76,77,78,91
2,3,19,42,45,57,70,76,84,90
2,3,19,42,48,57,70,76,80,84
2,3,19,42,50,57,70,75,76,84
2,3,19,42,55,57,66,70,76,84
2,3,19,42,56,57,60,72,76,90
2,3,19,42,56,57,63,72,76,84
2,3,19,44,45,57,70,76,77,90
2,3,19,44,48,57,70,76,77,80
2,3,19,44,50,57,70,75,76,77
2,3,19,44,55,57,66,70,76,77
2,3,19,44,56,57,63,72,76,77
2,3,19,45,48,57,60,76,80,90
2,3,19,45,48,57,63,76,80,84
2,3,19,45,50,57,60,75,76,90
2,3,19,45,50,57,63,75,76,84
2,3,19,45,55,57,60,66,76,90
2,3,19,45,55,57,63,66,76,84
2,3,19,48,50,57,60,75,76,80
2,3,19,48,55,57,60,66,76,80
2,3,19,50,55,57,60,66,75,76
2,3,20,22,70,78,84,90,91,99
2,3,20,24,66,70,77,88,90,99
2,3,20,24,70,72,78,84,90,91
2,3,20,25,55,70,77,90,99,100
2,3,20,25,56,72,78,90,91,100
2,3,20,25,60,70,78,84,91,100
2,3,20,27,54,70,78,84,90,91
2,3,20,28,55,60,77,84,90,99
2,3,20,28,55,63,77,78,91,99
2,3,20,28,56,70,72,78,90,91
2,3,20,30,45,70,78,84,90,91
2,3,20,30,48,70,78,80,84,91
2,3,20,30,50,70,75,78,84,91
2,3,20,30,55,60,70,77,90,99
2,3,20,30,55,63,70,77,84,99
2,3,20,30,55,66,70,78,84,91
2,3,20,30,56,60,72,78,90,91
2,3,20,30,56,63,66,77,88,99
2,3,20,30,56,63,72,78,84,91
2,3,20,32,38,72,76,90,95,96
2,3,20,32,40,70,78,84,91,96
2,3,20,32,42,70,72,84,90,96
2,3,20,32,44,70,72,77,90,96
2,3,20,32,45,56,78,90,91,96
2,3,20,32,45,63,72,84,90,96
2,3,20,32,48,56,78,80,91,96
2,3,20,32,48,60,72,80,90,96
2,3,20,32,48,63,72,80,84,96
2,3,20,32,50,56,75,78,91,96
2,3,20,32,50,60,72,75,90,96
2,3,20,32,50,63,72,75,84,96
2,3,20,32,55,56,63,77,96,99
2,3,20,32,55,56,66,78,91,96
2,3,20,32,55,60,66,72,90,96
2,3,20,32,55,63,66,72,84,96
2,3,20,33,38,66,76,90,95,99
2,3,20,33,38,72,76,88,90,95
2,3,20,33,40,70,78,84,88,91
2,3,20,33,42,66,70,84,90,99
2,3,20,33,42,70,72,84,88,90
2,3,20,33,44,66,70,77,90,99
2,3,20,33,44,70,72,77,88,90
2,3,20,33,45,56,78,88,90,91
2,3,20,33,45,63,66,84,90,99
2,3,20,33,45,63,72,84,88,90
2,3,20,33,48,56,78,80,88,91
2,3,20,33,48,60,66,80,90,99
2,3,20,33,48,60,72,80,88,90
2,3,20,33,48,63,66,80,84,99
2,3,20,33,48,63,72,80,84,88
2,3,20,33,50,56,75,78,88,91
2,3,20,33,50,60,66,75,90,99
2,3,20,33,50,60,72,75,88,90
2,3,20,33,50,63,66,75,84,99
2,3,20,33,50,63,72,75,84,88
2,3,20,33,55,56,63,77,88,99
2,3,20,33,55,56,66,78,88,91
2,3,20,33,55,60,66,72,88,90
2,3,20,33,55,63,66,72,84,88
2,3,20,35,38,70,76,78,91,95
2,3,20,35,40,70,72,78,90,91
2,3,20,35,42,55,77,84,90,99
2,3,20,35,44,60,77,78,84,91
2,3,20,35,45,60,70,78,90,91
2,3,20,35,45,63,70,78,84,91
2,3,20,35,48,56,72,80,84,90
2,3,20,35,48,60,70,78,80,91
2,3,20,35,50,56,72,75,84,90
2,3,20,35,50,60,70,75,78,91
2,3,20,35,55,56,66,72,84,90
2,3,20,35,55,60,63,70,77,99
2,3,20,35,55,60,66,70,78,91
2,3,20,35,56,60,63,72,78,91
2,3,20,36,38,63,76,84,90,95
2,3,20,36,40,66,70,77,88,99
2,3,20,36,40,70,72,78,84,91
2,3,20,36,42,55,77,78,91,99
2,3,20,36,42,63,70,78,90,91
2,3,20,36,44,63,70,77,84,90
2,3,20,36,45,55,70,77,90,99
2,3,20,36,45,56,72,78,90,91
2,3,20,36,45,60,70,78,84,91
2,3,20,36,48,55,70,77,80,99
2,3,20,36,48,56,72,78,80,91
2,3,20,36,48,60,63,80,84,90
2,3,20,36,50,55,70,75,77,99
2,3,20,36,50,56,72,75,78,91
2,3,20,36,50,60,63,75,84,90
2,3,20,36,55,56,63,72,77,99
2,3,20,36,55,56,66,72,78,91
2,3,20,36,55,60,63,66,84,90
2,3,20,38,40,56,76,78,91,95
2,3,20,38,40,60,72,76,90,95
2,3,20,38,40,63,72,76,84,95
2,3,20,38,42,56,72,76,90,95
2,3,20,38,42,60,70,76,84,95
2,3,20,38,44,60,70,76,77,95
2,3,20,38,45,48,76,80,90,95
2,3,20,38,45,50,75,76,90,95
2,3,20,38,45,55,66,76,90,95
2,3,20,38,45,60,63,76,84,95
2,3,20,38,48,50,75,76,80,95
2,3,20,38,48,55,66,76,80,95
2,3,20,38,50,55,66,75,76,95
2,3,20,40,42,56,70,78,84,91
2,3,20,40,42,60,70,72,84,90
2,3,20,40,42,63,70,72,78,91
2,3,20,40,44,56,70,77,78,91
2,3,20,40,44,60,70,72,77,90
2,3,20,40,44,63,70,72,77,84
2,3,20,40,45,55,70,72,77,99
2,3,20,40,45,56,60,78,90,91
2,3,20,40,45,56,63,78,84,91
2,3,20,40,45,60,63,72,84,90
2,3,20,40,48,50,72,75,80,90
2,3,20,40,48,55,66,72,80,90
2,3,20,40,48,56,60,78,80,91
2,3,20,40,48,60,63,72,80,84
2,3,20,40,50,55,66,72,75,90
2,3,20,40,50,56,60,75,78,91
2,3,20,40,50,60,63,72,75,84
2,3,20,40,55,56,60,63,77,99
2,3,20,40,55,56,60,66,78,91
2,3,20,40,55,60,63,66,72,84
2,3,20,42,44,45,77,78,90,91
2,3,20,42,44,48,77,78,80,91
2,3,20,42,44,50,75,77,78,91
2,3,20,42,44,55,66,77,78,91
2,3,20,42,44,56,70,72,77,90
2,3,20,42,45,48,70,80,84,90
2,3,20,42,45,50,70,75,84,90
2,3,20,42,45,55,66,70,84,90
2,3,20,42,45,56,63,72,84,90
2,3,20,42,45,60,63,70,78,91
2,3,20,42,48,50,70,75,80,84
2,3,20,42,48,55,66,70,80,84
2,3,20,42,48,56,60,72,80,90
2,3,20,42,48,56,63,72,80,84
2,3,20,42,50,55,66,70,75,84
2,3,20,42,50,56,60,72,75,90
2,3,20,42,50,56,63,72,75,84
2,3,20,42,55,56,60,66,72,90
2,3,20,42,55,56,63,66,72,84
2,3,20,44,45,48,70,77,80,90
2,3,20,44,45,50,70,75,77,90
2,3,20,44,45,55,66,70,77,90
2,3,20,44,45,56,63,72,77,90
2,3,20,44,45,60,63,70,77,84
2,3,20,44,48,50,70,75,77,80
2,3,20,44,48,55,66,70,77,80
2,3,20,44,48,56,63,72,77,80
2,3,20,44,50,55,66,70,75,77
2,3,20,44,50,56,63,72,75,77
2,3,20,44,55,56,63,66,72,77
2,3,20,45,48,50,60,75,80,90
2,3,20,45,48,50,63,75,80,84
2,3,20,45,48,55,60,66,80,90
2,3,20,45,48,55,63,66,80,84
2,3,20,45,50,55,60,66,75,90
2,3,20,45,50,55,63,66,75,84
2,3,20,48,50,55,60,66,75,80
2,3,21,22,60,78,84,90,91,99
2,3,21,24,60,66,77,88,90,99
2,3,21,24,60,72,78,84,90,91
2,3,21,24,63,66,77,84,88,99
2,3,21,25,45,78,84,90,91,100
2,3,21,25,48,78,80,84,91,100
2,3,21,25,50,75,78,84,91,100
2,3,21,25,55,60,77,90,99,100
2,3,21,25,55,63,77,84,99,100
2,3,21,25,55,66,78,84,91,100
2,3,21,25,56,70,72,84,90,100
2,3,21,26,55,65,77,78,90,99
2,3,21,27,54,60,78,84,90,91
2,3,21,27,54,66,72,77,88,99
2,3,21,28,45,70,78,84,90,91
2,3,21,28,48,70,78,80,84,91
2,3,21,28,50,70,75,78,84,91
2,3,21,28,55,60,70,77,90,99
2,3,21,28,55,63,70,77,84,99
2,3,21,28,55,66,70,78,84,91
2,3,21,28,56,60,72,78,90,91
2,3,21,28,56,63,66,77,88,99
2,3,21,28,56,63,72,78,84,91
2,3,21,30,38,76,78,84,91,95
2,3,21,30,40,66,77,88,90,99
2,3,21,30,40,72,78,84,90,91
2,3,21,30,44,70,77,78,84,91
2,3,21,30,45,60,78,84,90,91
2,3,21,30,45,66,72,77,88,99
2,3,21,30,48,55,77,80,90,99
2,3,21,30,48,60,78,80,84,91
2,3,21,30,50,55,75,77,90,99
2,3,21,30,50,60,75,78,84,91
2,3,21,30,55,60,63,77,84,99
2,3,21,30,55,60,66,78,84,91
2,3,21,30,56,60,70,72,84,90
2,3,21,30,56,63,70,72,78,91
2,3,21,32,33,78,84,88,91,96
2,3,21,32,35,72,78,90,91,96
2,3,21,32,36,66,77,88,96,99
2,3,21,32,36,72,78,84,91,96
2,3,21,32,40,55,77,90,96,99
2,3,21,32,40,60,78,84,91,96
2,3,21,32,42,56,78,84,91,96
2,3,21,32,42,60,72,84,90,96
2,3,21,32,42,63,72,78,91,96
2,3,21,32,44,56,77,78,91,96
2,3,21,32,44,60,72,77,90,96
2,3,21,32,44,63,72,77,84,96
2,3,21,32,45,55,72,77,96,99
2,3,21,32,45,56,70,84,90,96
2,3,21,32,45,63,70,72,90,96
2,3,21,32,48,56,70,80,84,96
2,3,21,32,48,63,70,72,80,96
2,3,21,32,50,56,70,75,84,96
2,3,21,32,50,63,70,72,75,96
2,3,21,32,55,56,66,70,84,96
2,3,21,32,55,63,66,70,72,96
2,3,21,33,35,66,78,90,91,99
2,3,21,33,35,72,78,88,90,91
2,3,21,33,36,66,78,84,91,99
2,3,21,33,36,72,78,84,88,91
2,3,21,33,40,55,77,88,90,99
2,3,21,33,40,60,78,84,88,91
2,3,21,33,42,56,78,84,88,91
2,3,21,33,42,60,66,84,90,99
2,3,21,33,42,60,72,84,88,90
2,3,21,33,42,63,66,78,91,99
2,3,21,33,42,63,72,78,88,91
2,3,21,33,44,56,77,78,88,91
2,3,21,33,44,60,66,77,90,99
2,3,21,33,44,60,72,77,88,90
2,3,21,33,44,63,66,77,84,99
2,3,21,33,44,63,72,77,84,88
2,3,21,33,45,55,72,77,88,99
2,3,21,33,45,56,70,84,88,90
2,3,21,33,45,63,66,70,90,99
2,3,21,33,45,63,70,72,88,90
2,3,21,33,48,56,70,80,84,88
2,3,21,33,48,63,66,70,80,99
2,3,21,33,48,63,70,72,80,88
2,3,21,33,50,56,70,75,84,88
2,3,21,33,50,63,66,70,75,99
2,3,21,33,50,63,70,72,75,88
2,3,21,33,55,56,66,70,84,88
2,3,21,33,55,63,66,70,72,88
2,3,21,35,36,63,78,84,90,91
2,3,21,35,38,60,76,78,91,95
2,3,21,35,40,60,72,78,90,91
2,3,21,35,40,63,66,77,88,99
2,3,21,35,40,63,72,78,84,91
2,3,21,35,42,55,70,77,90,99
2,3,21,35,42,56,72,78,90,91
2,3,21,35,42,60,70,78,84,91
2,3,21,35,44,56,72,77,84,90
2,3,21,35,44,60,70,77,78,91
2,3,21,35,45,48,78,80,90,91
2,3,21,35,45,50,75,78,90,91
2,3,21,35,45,55,63,77,90,99
2,3,21,35,45,55,66,78,90,91
2,3,21,35,45,60,63,78,84,91
2,3,21,35,48,50,75,78,80,91
2,3,21,35,48,55,63,77,80,99
2,3,21,35,48,55,66,78,80,91
2,3,21,35,48,56,70,72,80,90
2,3,21,35,50,55,63,75,77,99
2,3,21,35,50,55,66,75,78,91
2,3,21,35,50,56,70,72,75,90
2,3,21,35,55,56,66,70,72,90
2,3,21,35,56,60,63,70,72,84
2,3,21,36,38,55,76,77,95,99
2,3,21,36,38,63,70,76,90,95
2,3,21,36,40,55,72,77,90,99
2,3,21,36,40,60,66,77,88,99
2,3,21,36,40,60,72,78,84,91
2,3,21,36,42,55,70,77,84,99
2,3,21,36,42,56,66,77,88,99
2,3,21,36,42,56,72,78,84,91