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# [分享] 1~9填入宫格，使等式成立

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x
Qu.1
\(\Huge
\square+\dfrac{\square}{\square}+\dfrac{\square\square\square}{\square\square\square}=10
\)
Qu.2
\(\Huge
\dfrac{\square}{\square}+\dfrac{\square\square}{\square}+\dfrac{\square\square}{\square\square}=10
\)

 1. {3,5,1,9,7,2,4,8,6} {4,9,3,5,2,8,1,7,6} {5,3,1,9,7,2,4,8,6} {5,4,3,7,2,6,1,9,8} {5,4,9,7,3,8,1,6,2} {5,8,6,4,7,3,1,2,9} {6,4,2,3,5,8,1,7,9} {6,4,2,7,1,8,3,5,9} {6,7,3,4,8,5,2,9,1} {6,8,3,9,5,2,7,1,4} {6,9,8,4,3,7,1,5,2} {7,1,4,9,6,8,3,5,2} {7,3,2,8,1,9,5,4,6} {7,3,2,9,8,1,6,5,4} {7,5,3,2,6,4,1,9,8} {7,5,3,9,1,2,6,8,4} {7,9,6,3,8,1,2,5,4} {7,9,6,8,1,3,5,4,2} {8,1,3,4,6,5,2,7,9} {8,6,9,7,1,2,5,3,4} {8,7,6,1,9,5,2,3,4} {9,1,3,4,5,2,6,7,8} {9,1,3,5,2,4,7,8,6} {9,2,4,1,7,8,3,5,6} {9,2,4,3,5,8,7,1,6} {9,3,4,1,5,7,6,2,8} {9,4,8,1,7,6,3,5,2} {9,4,8,3,5,6,7,1,2} {9,6,8,1,4,3,5,7,2} 2. {1,2,4,5,6,7,8,3,9} {1,2,5,4,6,3,9,7,8} {1,2,6,4,7,3,5,9,8} {1,3,4,9,6,7,8,5,2} {1,4,5,9,8,7,6,3,2} {1,6,7,5,9,4,8,3,2} {1,8,2,7,3,4,9,5,6} {1,8,3,5,6,9,7,2,4} {2,1,4,5,6,3,9,7,8} {2,1,5,4,9,7,6,3,8} {2,3,5,7,9,4,8,1,6} {2,4,7,1,9,5,8,3,6} {2,7,8,1,9,4,5,6,3} {2,9,4,7,6,3,5,1,8} {3,6,7,2,9,8,1,5,4} {3,6,8,1,9,2,7,5,4} {3,9,1,7,2,5,6,4,8} {3,9,2,6,4,5,7,1,8} {3,9,4,5,7,6,8,2,1} {3,9,5,1,6,8,4,7,2} {3,9,5,4,6,1,8,2,7} {3,9,5,7,8,6,1,2,4} {4,3,5,1,9,7,8,2,6} {5,1,2,7,9,6,8,3,4} {5,1,2,7,9,8,6,4,3} {5,1,3,4,8,7,2,9,6} {5,2,3,4,9,6,7,1,8} {5,2,4,9,7,1,8,3,6} {5,3,7,2,9,1,6,4,8} {5,6,2,4,3,9,1,7,8} {5,6,3,2,4,9,1,7,8} {5,7,6,3,9,4,8,2,1} {5,8,1,6,3,9,7,2,4} {5,8,3,7,4,1,2,9,6} {5,9,3,2,6,7,4,1,8} {6,1,2,3,9,7,8,5,4} {6,3,4,5,9,8,1,2,7} {6,9,2,7,3,1,8,5,4} {7,2,1,6,4,9,5,3,8} {7,2,3,6,9,4,5,1,8} {7,2,5,4,9,1,8,3,6} {7,4,1,3,2,9,8,5,6} {7,8,3,1,6,9,5,2,4} {7,8,6,3,9,5,1,2,4} {7,9,2,6,3,4,5,8,1} {8,2,3,4,6,1,9,5,7} {8,3,4,2,6,1,9,5,7} {8,4,2,7,9,6,5,1,3} {8,4,5,1,9,6,3,2,7} {8,6,4,9,7,3,5,2,1} {8,6,7,2,9,3,4,5,1} {9,2,1,4,3,6,5,7,8} {9,2,1,6,4,5,7,3,8} {9,3,2,7,6,4,5,1,8} {9,3,4,5,7,1,6,2,8} {9,6,1,4,2,5,7,3,8} {9,6,5,1,7,3,4,2,8} {9,6,5,2,8,3,4,1,7}

### 评分

gxqcn + 6 + 6 赞一个!

 2# 楼计算结果有的不对。例如 {3,5,1,9,7,2,4,8,6} 的结果是 3+5/1+972/486=3+5+27/13= 131/13， 不等于 10。 请 2# 把程序贴出来看看。

 TSC999 发表于 2018-7-14 20:15 2# 楼计算结果有的不对。例如 {3,5,1,9,7,2,4,8,6} 的结果是 3+5/1+972/486=3+5+27/13= 131/13， 不等于 10 ... 972/486=2

### 点评

 本帖最后由 TSC999 于 2018-7-14 21:53 编辑 aa = Permutations[{1, 2, 3, 4, 5, 6, 7, 8, 9}] ; For[i = 1, i <= 362880, i++, a = aa[[i]]; If[a[[1]] + a[[2]]/a[[3]] + (100 a[[4]] + 10 a[[5]] + a[[6]])/(     100 a[[7]] + 10 a[[8]] + a[[9]]) == 10, Print[a]]; ]复制代码 运行结果是： {3,5,1,9,7,2,4,8,6} {4,9,3,5,2,8,1,7,6} {5,3,1,9,7,2,4,8,6} {5,4,3,7,2,6,1,9,8} {5,4,9,7,3,8,1,6,2} {5,8,6,4,7,3,1,2,9} {6,4,2,3,5,8,1,7,9} {6,4,2,7,1,8,3,5,9} {6,7,3,4,8,5,2,9,1} {6,8,3,9,5,2,7,1,4} {6,9,8,4,3,7,1,5,2} {7,1,4,9,6,8,3,5,2} {7,3,2,8,1,9,5,4,6} {7,3,2,9,8,1,6,5,4} {7,5,3,2,6,4,1,9,8} {7,5,3,9,1,2,6,8,4} {7,9,6,3,8,1,2,5,4} {7,9,6,8,1,3,5,4,2} {8,1,3,4,6,5,2,7,9} {8,6,9,7,1,2,5,3,4} {8,7,6,1,9,5,2,3,4} {9,1,3,4,5,2,6,7,8} {9,1,3,5,2,4,7,8,6} {9,2,4,1,7,8,3,5,6} {9,2,4,3,5,8,7,1,6} {9,3,4,1,5,7,6,2,8} {9,4,8,1,7,6,3,5,2} {9,4,8,3,5,6,7,1,2} {9,6,8,1,4,3,5,7,2}

### 点评

 我这个程序大概不是很好，如何优化？

 本帖最后由 zeroieme 于 2018-7-14 23:30 编辑 9//Range//Permutations//ParallelCombine[Select[#,#[[1]]+#[[2]]/#[[3]]+(100#[[4]]+10#[[5]]+#[[6]])/(100#[[7]]+10#[[8]]+#[[9]])==10&]&,#]&复制代码 9//Range//Permutations//ParallelCombine[Select[#,#[[1]]/#[[2]]+(10#[[3]]+#[[4]])/#[[5]]+(10#[[6]]+#[[7]])/(10#[[8]]+#[[9]])==10&]&,#]&复制代码

### 点评

 一点想法：假设每个商都是正整数，那么5一定不能出现在除数的末位上。

### 点评

 TSC999 发表于 2018-7-14 21:52 运行结果是： {3,5,1,9,7,2,4,8,6}Permutations[Range[9]]//Pick[#,Table[p[[1]]+p[[2]]/p[[3]]+(100 p[[4]]+10 p[[5]]+p[[6]])/(100 p[[7]]+10 p[[8]]+p[[9]])-10//N//Unitize,{p,#}],0]&//AbsoluteTiming复制代码

### 点评

N是关键！  发表于 2018-7-16 10:48

楼主| 发表于 2020-9-11 18:20:42 | 显示全部楼层
 mark一下类似题目 [分享] 简单填数--极限玩法 2010-1-5 08:55:22 https://bbs.emath.ac.cn/forum.php?mod=viewthread&tid=2049

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