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Sounds like a dynamic programming problem. Specifically, this sounds like a variation of longest increasing subsequence. The Papadimitriou Algorithms textbook (which you can easily google online, but which I'm not allowed to post the link to here) offers a fundamental understanding of how to solve longest increasing subsequence. Page 162 I think. It's then pretty trivial to adapt the the algorithm to longest decreasing subsequence of evens.
- foxjas09 January 03, 2015