Inspired by Project Euler

Number Theory Level 5

Define \(\text{reverse}(n)\) as a function which reverses the given integer. For example, \(\text{reverse}(23)=32\) and \(\text{reverse}(405)=504\).

Now, some natural numbers \(n\) have a property that \(n+\text{reverse}(n)\) always consists of odd digits. For example, \(36+\text{reverse}(36)=36+63=99\) and \(409+\text{reverse}(409)=409+904=1313\).

We call such numbers Reversible Numbers. Thus, \(36,63,409,904\) are Reversible Numbers.

Calculate the total number of Reversible numbers less than \(10^{11}\).

Details and Assumptions:

  • Leading zeroes are NOT allowed in \(n\) or \(\text{reverse}(n)\).

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