数学研发论坛

 找回密码
 欢迎注册
查看: 337|回复: 16

[分享] 1~9填入宫格,使等式成立

[复制链接]
发表于 2018-7-11 10:44:08 | 显示全部楼层 |阅读模式

马上注册,结交更多好友,享用更多功能,让你轻松玩转社区。

您需要 登录 才可以下载或查看,没有帐号?欢迎注册

x
Qu.1
\(\Huge
\square+\dfrac{\square}{\square}+\dfrac{\square\square\square}{\square\square\square}=10
\)
Qu.2
\(\Huge
\dfrac{\square}{\square}+\dfrac{\square\square}{\square}+\dfrac{\square\square}{\square\square}=10
\)
毋因群疑而阻独见  毋任己意而废人言
毋私小惠而伤大体  毋借公论以快私情
发表于 2018-7-12 16:40:03 | 显示全部楼层
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

参与人数 1贡献 +6 鲜花 +6 收起 理由
gxqcn + 6 + 6 赞一个!

查看全部评分

毋因群疑而阻独见  毋任己意而废人言
毋私小惠而伤大体  毋借公论以快私情
发表于 2018-7-14 20:15:51 | 显示全部楼层
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。
毋因群疑而阻独见  毋任己意而废人言
毋私小惠而伤大体  毋借公论以快私情
发表于 2018-7-14 21:35:21 | 显示全部楼层
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

噢,是我弄错了!  发表于 2018-7-14 21:51
毋因群疑而阻独见  毋任己意而废人言
毋私小惠而伤大体  毋借公论以快私情
发表于 2018-7-14 21:52:36 | 显示全部楼层
本帖最后由 TSC999 于 2018-7-14 21:53 编辑
  1. aa = Permutations[{1, 2, 3, 4, 5, 6, 7, 8, 9}] ;
  2. For[i = 1, i <= 362880, i++,
  3. a = aa[[i]];
  4. If[a[[1]] + a[[2]]/a[[3]] + (100 a[[4]] + 10 a[[5]] + a[[6]])/(
  5.     100 a[[7]] + 10 a[[8]] + a[[9]]) == 10, Print[a]];
  6. ]
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

上面程序运行时间是4.6秒。  发表于 2018-7-16 06:00
毋因群疑而阻独见  毋任己意而废人言
毋私小惠而伤大体  毋借公论以快私情
发表于 2018-7-14 21:55:59 | 显示全部楼层
我这个程序大概不是很好,如何优化?
毋因群疑而阻独见  毋任己意而废人言
毋私小惠而伤大体  毋借公论以快私情
发表于 2018-7-14 23:25:47 | 显示全部楼层
本帖最后由 zeroieme 于 2018-7-14 23:30 编辑
  1. 9//Range//Permutations//ParallelCombine[Select[#,#[[1]]+#[[2]]/#[[3]]+(100#[[4]]+10#[[5]]+#[[6]])/(100#[[7]]+10#[[8]]+#[[9]])==10&]&,#]&
复制代码

  1. 9//Range//Permutations//ParallelCombine[Select[#,#[[1]]/#[[2]]+(10#[[3]]+#[[4]])/#[[5]]+(10#[[6]]+#[[7]])/(10#[[8]]+#[[9]])==10&]&,#]&
复制代码

点评

这两个程序运行时间是8.6秒和6.1秒。对否?【在我的破机器上运行的时间】  发表于 2018-7-16 05:56
毋因群疑而阻独见  毋任己意而废人言
毋私小惠而伤大体  毋借公论以快私情
发表于 2018-7-15 08:30:39 | 显示全部楼层
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

商不是正整数也对的。除数的末位是5,则这个商带因子\(1/5\)。然而没有另一个也带因子\(1/5\)的商与之合并消除。  发表于 2018-7-15 11:32
可是有些商不是正整数的情况也存在。  发表于 2018-7-15 08:31
毋因群疑而阻独见  毋任己意而废人言
毋私小惠而伤大体  毋借公论以快私情
发表于 2018-7-15 14:36:09 | 显示全部楼层
TSC999 发表于 2018-7-14 21:52
运行结果是:

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

关键的不只是N,主要是这里用Table会自动Compile,楼上的代码即使加了N速度提升也很小  发表于 2018-7-22 21:39
N是关键!  发表于 2018-7-16 10:48
这个程序运行速度非常快,0.17 秒!  发表于 2018-7-16 05:57
毋因群疑而阻独见  毋任己意而废人言
毋私小惠而伤大体  毋借公论以快私情
您需要登录后才可以回帖 登录 | 欢迎注册

本版积分规则

小黑屋|手机版|数学研发网 ( 苏ICP备07505100号 )

GMT+8, 2018-9-23 20:36 , Processed in 2.022886 second(s), 17 queries .

Powered by Discuz! X3.4

© 2001-2017 Comsenz Inc.

快速回复 返回顶部 返回列表