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K-digits

Source: Chinese TST 2007 3rd quiz P2

January 3, 2009
combinatorics proposedcombinatorics

Problem Statement

Given an integer k>1. k > 1. We call a k \minus{}digits decimal integer a1a2⋯ak a_{1}a_{2}\cdots a_{k} is p \minus{}monotonic, if for each of integers i i satisfying 1\le i\le k \minus{} 1, when ai a_{i} is an odd number, a_{i} > a_{i \plus{} 1}; when ai a_{i} is an even number, a_{i}
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