HMMT 2007 C2

Combinatorics
Answer

How many 5-digit numbers $\overline{a b c d e}$ exist such that digits $b$ and $d$ are each the sum of the digits to their immediate left and right? (That is, $b=a+c$ and $d=c+e$ .)

Dataset text NuminaMath olympiads. Quoted with source.

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