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题目是这样的:
2015年5月24日讯,越南数学题难倒博士,据外国媒体报道,近日网络上竟然出现一道神题,据称这是给越南三年级、8岁小学生做的数学难题,不过却是难道了下至家长上至博士,到底这道题的难度在哪?
据悉题目来自越南保禄小学三年班,学生需要由上至下、从左到右的顺序,填入1至9的数字,可重复填写,并按先乘除后加减的运算法则,完成整条算式。
求解方法:
我通过穷举法编程求解发现该道题一共有442232种答案,所有组合有9的9次方种,随便写一种答案答对的概率为0.11%。命题小老头真可爱,几十万种答案,居然参考答案只有几种。你怎么不问小学生有多少种答案,或者问如果1到9每个数字只能用一次又有多少种答案。
其实这个题要得出几种答案并不是很难,只需要将乘除连接的地方尝试法调整,最后一个数一定要在1到9之间,然后可转化为几个数的和为66,便可以得出答案。
所有答案下载地址:http://pan.baidu.com/s/1dDwCGxF
通过编程求解,程序如下:
clc;
clear;
close all;
ans=[];
for a=1:9
for b=1:9
for c=1:9
for d=1:9
for e=1:9
for f=1:9
for g=1:9
for h=1:9
for i=1:9
result=a+13*b/c+d+12*e-f-11+g*h/i-10;
if result==66;
answer=[a b c d e f g h i]; ans=[ans;answer];
end
end
end
end
end
end
end
end
end
end
所有答案下载地址:http://pan.baidu.com/s/1dDwCGxF
通过程序求解1-9只能用一次。
clc
clear
close all
load aa.mat
b=a;
cc=[];
for i=1:442232
dd=length(unique(b(i,:)));
ifdd==9
cc=[cc;b(i,:)];
end
end
1-9只能用一次,被细心的人给发现了,一共有128组,见表1。
表1 1-9只能用一次
1 | 2 | 6 | 4 | 7 | 8 | 3 | 5 | 9 |
1 | 2 | 6 | 4 | 7 | 8 | 5 | 3 | 9 |
1 | 3 | 2 | 4 | 5 | 8 | 7 | 9 | 6 |
1 | 3 | 2 | 4 | 5 | 8 | 9 | 7 | 6 |
1 | 3 | 2 | 9 | 5 | 6 | 4 | 7 | 8 |
1 | 3 | 2 | 9 | 5 | 6 | 7 | 4 | 8 |
1 | 3 | 4 | 7 | 6 | 5 | 2 | 9 | 8 |
1 | 3 | 4 | 7 | 6 | 5 | 9 | 2 | 8 |
1 | 3 | 6 | 2 | 7 | 9 | 4 | 5 | 8 |
1 | 3 | 6 | 2 | 7 | 9 | 5 | 4 | 8 |
1 | 3 | 9 | 4 | 7 | 8 | 2 | 5 | 6 |
1 | 3 | 9 | 4 | 7 | 8 | 5 | 2 | 6 |
1 | 4 | 8 | 2 | 7 | 9 | 3 | 5 | 6 |
1 | 4 | 8 | 2 | 7 | 9 | 5 | 3 | 6 |
1 | 5 | 2 | 3 | 4 | 8 | 7 | 9 | 6 |
1 | 5 | 2 | 3 | 4 | 8 | 9 | 7 | 6 |
1 | 5 | 2 | 8 | 4 | 7 | 3 | 9 | 6 |
1 | 5 | 2 | 8 | 4 | 7 | 9 | 3 | 6 |
1 | 5 | 3 | 9 | 4 | 2 | 7 | 8 | 6 |
1 | 5 | 3 | 9 | 4 | 2 | 8 | 7 | 6 |
1 | 9 | 6 | 4 | 5 | 8 | 3 | 7 | 2 |
1 | 9 | 6 | 4 | 5 | 8 | 7 | 3 | 2 |
1 | 9 | 6 | 7 | 5 | 2 | 3 | 4 | 8 |
1 | 9 | 6 | 7 | 5 | 2 | 4 | 3 | 8 |
2 | 1 | 4 | 3 | 7 | 9 | 5 | 6 | 8 |
2 | 1 | 4 | 3 | 7 | 9 | 6 | 5 | 8 |
2 | 3 | 6 | 1 | 7 | 9 | 4 | 5 | 8 |
2 | 3 | 6 | 1 | 7 | 9 | 5 | 4 | 8 |
2 | 4 | 8 | 1 | 7 | 9 | 3 | 5 | 6 |
2 | 4 | 8 | 1 | 7 | 9 | 5 | 3 | 6 |
2 | 8 | 6 | 9 | 4 | 1 | 5 | 7 | 3 |
2 | 8 | 6 | 9 | 4 | 1 | 7 | 5 | 3 |
2 | 9 | 6 | 3 | 5 | 1 | 4 | 7 | 8 |
2 | 9 | 6 | 3 | 5 | 1 | 7 | 4 | 8 |
3 | 1 | 4 | 2 | 7 | 9 | 5 | 6 | 8 |
3 | 1 | 4 | 2 | 7 | 9 | 6 | 5 | 8 |
3 | 2 | 1 | 5 | 4 | 7 | 8 | 9 | 6 |
3 | 2 | 1 | 5 | 4 | 7 | 9 | 8 | 6 |
3 | 2 | 4 | 8 | 5 | 1 | 7 | 9 | 6 |
3 | 2 | 4 | 8 | 5 | 1 | 9 | 7 | 6 |
3 | 2 | 8 | 6 | 5 | 1 | 7 | 9 | 4 |
3 | 2 | 8 | 6 | 5 | 1 | 9 | 7 | 4 |
3 | 5 | 2 | 1 | 4 | 8 | 7 | 9 | 6 |
3 | 5 | 2 | 1 | 4 | 8 | 9 | 7 | 6 |
3 | 6 | 4 | 9 | 5 | 8 | 1 | 7 | 2 |
3 | 6 | 4 | 9 | 5 | 8 | 7 | 1 | 2 |
3 | 9 | 2 | 8 | 1 | 5 | 6 | 7 | 4 |
3 | 9 | 2 | 8 | 1 | 5 | 7 | 6 | 4 |
3 | 9 | 6 | 2 | 5 | 1 | 4 | 7 | 8 |
3 | 9 | 6 | 2 | 5 | 1 | 7 | 4 | 8 |
4 | 2 | 6 | 1 | 7 | 8 | 3 | 5 | 9 |
4 | 2 | 6 | 1 | 7 | 8 | 5 | 3 | 9 |
4 | 3 | 2 | 1 | 5 | 8 | 7 | 9 | 6 |
4 | 3 | 2 | 1 | 5 | 8 | 9 | 7 | 6 |
4 | 3 | 9 | 1 | 7 | 8 | 2 | 5 | 6 |
4 | 3 | 9 | 1 | 7 | 8 | 5 | 2 | 6 |
4 | 9 | 6 | 1 | 5 | 8 | 3 | 7 | 2 |
4 | 9 | 6 | 1 | 5 | 8 | 7 | 3 | 2 |
5 | 1 | 2 | 9 | 6 | 7 | 3 | 4 | 8 |
5 | 1 | 2 | 9 | 6 | 7 | 4 | 3 | 8 |
5 | 2 | 1 | 3 | 4 | 7 | 8 | 9 | 6 |
5 | 2 | 1 | 3 | 4 | 7 | 9 | 8 | 6 |
5 | 3 | 1 | 7 | 2 | 6 | 8 | 9 | 4 |
5 | 3 | 1 | 7 | 2 | 6 | 9 | 8 | 4 |
5 | 4 | 1 | 9 | 2 | 7 | 3 | 8 | 6 |
5 | 4 | 1 | 9 | 2 | 7 | 8 | 3 | 6 |
5 | 4 | 8 | 9 | 6 | 7 | 1 | 3 | 2 |
5 | 4 | 8 | 9 | 6 | 7 | 3 | 1 | 2 |
5 | 7 | 2 | 8 | 3 | 9 | 1 | 6 | 4 |
5 | 7 | 2 | 8 | 3 | 9 | 6 | 1 | 4 |
5 | 9 | 3 | 6 | 2 | 1 | 7 | 8 | 4 |
5 | 9 | 3 | 6 | 2 | 1 | 8 | 7 | 4 |
6 | 2 | 8 | 3 | 5 | 1 | 7 | 9 | 4 |
6 | 2 | 8 | 3 | 5 | 1 | 9 | 7 | 4 |
6 | 3 | 1 | 9 | 2 | 5 | 7 | 8 | 4 |
6 | 3 | 1 | 9 | 2 | 5 | 8 | 7 | 4 |
6 | 9 | 3 | 5 | 2 | 1 | 7 | 8 | 4 |
6 | 9 | 3 | 5 | 2 | 1 | 8 | 7 | 4 |
7 | 1 | 4 | 9 | 6 | 5 | 2 | 3 | 8 |
7 | 1 | 4 | 9 | 6 | 5 | 3 | 2 | 8 |
7 | 2 | 8 | 9 | 6 | 5 | 1 | 3 | 4 |
7 | 2 | 8 | 9 | 6 | 5 | 3 | 1 | 4 |
7 | 3 | 1 | 5 | 2 | 6 | 8 | 9 | 4 |
7 | 3 | 1 | 5 | 2 | 6 | 9 | 8 | 4 |
7 | 3 | 2 | 8 | 5 | 9 | 1 | 6 | 4 |
7 | 3 | 2 | 8 | 5 | 9 | 6 | 1 | 4 |
7 | 3 | 4 | 1 | 6 | 5 | 2 | 9 | 8 |
7 | 3 | 4 | 1 | 6 | 5 | 9 | 2 | 8 |
7 | 5 | 2 | 8 | 4 | 9 | 1 | 3 | 6 |
7 | 5 | 2 | 8 | 4 | 9 | 3 | 1 | 6 |
7 | 6 | 4 | 8 | 5 | 9 | 1 | 3 | 2 |
7 | 6 | 4 | 8 | 5 | 9 | 3 | 1 | 2 |
7 | 9 | 6 | 1 | 5 | 2 | 3 | 4 | 8 |
7 | 9 | 6 | 1 | 5 | 2 | 4 | 3 | 8 |
8 | 2 | 4 | 3 | 5 | 1 | 7 | 9 | 6 |
8 | 2 | 4 | 3 | 5 | 1 | 9 | 7 | 6 |
8 | 3 | 2 | 7 | 5 | 9 | 1 | 6 | 4 |
8 | 3 | 2 | 7 | 5 | 9 | 6 | 1 | 4 |
8 | 5 | 2 | 1 | 4 | 7 | 3 | 9 | 6 |
8 | 5 | 2 | 1 | 4 | 7 | 9 | 3 | 6 |
8 | 5 | 2 | 7 | 4 | 9 | 1 | 3 | 6 |
8 | 5 | 2 | 7 | 4 | 9 | 3 | 1 | 6 |
8 | 6 | 4 | 7 | 5 | 9 | 1 | 3 | 2 |
8 | 6 | 4 | 7 | 5 | 9 | 3 | 1 | 2 |
8 | 7 | 2 | 5 | 3 | 9 | 1 | 6 | 4 |
8 | 7 | 2 | 5 | 3 | 9 | 6 | 1 | 4 |
8 | 9 | 2 | 3 | 1 | 5 | 6 | 7 | 4 |
8 | 9 | 2 | 3 | 1 | 5 | 7 | 6 | 4 |
9 | 1 | 2 | 5 | 6 | 7 | 3 | 4 | 8 |
9 | 1 | 2 | 5 | 6 | 7 | 4 | 3 | 8 |
9 | 1 | 4 | 7 | 6 | 5 | 2 | 3 | 8 |
9 | 1 | 4 | 7 | 6 | 5 | 3 | 2 | 8 |
9 | 2 | 8 | 7 | 6 | 5 | 1 | 3 | 4 |
9 | 2 | 8 | 7 | 6 | 5 | 3 | 1 | 4 |
9 | 3 | 1 | 6 | 2 | 5 | 7 | 8 | 4 |
9 | 3 | 1 | 6 | 2 | 5 | 8 | 7 | 4 |
9 | 3 | 2 | 1 | 5 | 6 | 4 | 7 | 8 |
9 | 3 | 2 | 1 | 5 | 6 | 7 | 4 | 8 |
9 | 4 | 1 | 5 | 2 | 7 | 3 | 8 | 6 |
9 | 4 | 1 | 5 | 2 | 7 | 8 | 3 | 6 |
9 | 4 | 8 | 5 | 6 | 7 | 1 | 3 | 2 |
9 | 4 | 8 | 5 | 6 | 7 | 3 | 1 | 2 |
9 | 5 | 3 | 1 | 4 | 2 | 7 | 8 | 6 |
9 | 5 | 3 | 1 | 4 | 2 | 8 | 7 | 6 |
9 | 6 | 4 | 3 | 5 | 8 | 1 | 7 | 2 |
9 | 6 | 4 | 3 | 5 | 8 | 7 | 1 | 2 |
9 | 8 | 6 | 2 | 4 | 1 | 5 | 7 | 3 |
9 | 8 | 6 | 2 | 4 | 1 | 7 | 5 | 3 |
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