Problem 145
How many reversible numbers are there below one-billion?
Some positive integers n have the property that the sum [ n + reverse(n) ] consists entirely of odd (decimal) digits. For instance, 36 + 63 = 99 and 409 + 904 = 1313. We will call such numbers reversible; so 36, 63, 409, and 904 are reversible. Leading zeroes are not allowed in either n or reverse(n).
There are 120 reversible numbers below one-thousand.
How many reversible numbers are there below one-billion (109)?
有多少小于十亿的可逆数？
有些正整数n满足这样一种性质，将它的数字逆序排列后和本身相加所得到的和[ n + reverse(n) ]的十进制表示只包含有奇数数字。例如，36 + 63 = 99 以及409 + 904 = 1313。我们称这样的数是可逆的；因此36，63，409和904都是可逆的。无论是n还是reverse(n)都不允许出现前导0。
在小于一千的数中，一共有120个可逆数。
在小于十亿（109）的数中，一共有多少个可逆数？