# Inspired by Project Euler

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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