# Problem 145: How many reversible numbers are there below one-billion?

![graphic](img145.gif)

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)?