从0到9十个数谁能得出一个加法运算十个数都要用

Question

从0到9十个数谁能得出一个加法运算
十个数都要用

Answer 1

解题大概思路：
两个三位数之和得到的4位数其最高位必定为1,且两个三位数至少有一个最高位不小于5,这样题目转化为：
□□□+□□□=1□□□
将等号右边的3个框移到左边,则：
□□□+□□□-□□□=1000
于是题目等价变为
a1a2a3+b1b2b3-c1c2c3=1000
注意到两个3位数做加法,不妨设a1≥5.这样即可展开讨论.
我们很容易获得了24组结果,依次填写顺序为：
8,2,4,6,7,9,1,5,0,3
8,2,6,4,7,9,1,3,0,5
8,2,9,4,7,6,1,3,0,5
8,2,9,6,7,4,1,5,0,3
8,4,3,7,5,9,1,6,0,2
8,4,7,3,5,9,1,2,0,6
8,4,9,3,5,7,1,2,0,6
8,4,9,7,5,3,1,6,0,2
8,5,3,7,4,9,1,6,0,2
8,5,7,3,4,9,1,2,0,6
8,5,9,3,4,7,1,2,0,6
8,5,9,7,4,3,1,6,0,2
8,7,4,6,2,9,1,5,0,3
8,7,6,4,2,9,1,3,0,5
8,7,9,4,2,6,1,3,0,5
8,7,9,6,2,4,1,5,0,3
-------------------
7,4,3,8,5,9,1,6,0,2
7,4,9,8,5,3,1,6,0,2
7,5,3,8,4,9,1,6,0,2
7,5,9,8,4,3,1,6,0,2
-------------------
6,2,4,8,7,9,1,5,0,3
6,2,9,8,7,4,1,5,0,3
6,7,4,8,2,9,1,5,0,3
6,7,9,8,2,4,1,5,0,3