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Parity-Monotonic Numbers

Source: AIME II 2007 #6

March 29, 2007
AMCAIMEAoPSwikiAIME IIAIME I

Problem Statement

An integer is called parity-monotonic if its decimal representation a1a2a3⋯aka_{1}a_{2}a_{3}\cdots a_{k} satisfies ai<ai+1a_{i}<a_{i+1} if aia_{i} is odd, and ai>ai+1a_{i}>a_{i+1} is aia_{i} is even. How many four-digit parity-monotonic integers are there?
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