猴哥112第6题

lizaozaoUID: 3137052

The "reflection" of a positive integer is obtained by reversing its digits. For example, 321 is the reflection of 123. The difference between a five-digit integer and its reflection must be divisible by which of the following?

ANSWERS-
2
4
5
6
9<-----Real Answer

lizaozaoUID: 3137052

我做的时候代入了几个数试了三回，基本靠蒙。
后来在urch论坛找到了靠谱答案。

x = a * 10000 + b * 1000 + c * 100 + d * 10 + e
y = e * 10000 + d * 1000 + c * 100 + b * 10 + a

Then y - x is:

y - x = e * 9999 + d * 990 + b * (-990) + a * (-9999)
= 9 [e * 1111 + d * 110 + b * (-110) + a * (-1111)]

lizaozaoUID: 3137052

最简单的是10000和1的差9999
palesaint 发表于 2011-11-1 20:04

哇，这一招真好。

lionelfengUID: 2371460

最简单的是10000和1的差9999
palesaint 发表于 2011-11-1 20:04