## How many reversible numbers are there below one-billion?

### Problem 145

Published on Friday, 16th March 2007, 01:00 pm; Solved by 10436; Difficulty rating: 20%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 (10^{9})?