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a Construct a sequence of length 16 consisting of the numbers 1 2 16 each occurring once that has no increasing subsequence of length five

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a Construct a sequence of length 16 consisting of the numbers 1 2 16 each occurring once that has no increasing subsequence of length five and also no decreasing subsequence of length five Prove that every sequence of length 17 consisting of the numbers 1 2 17 each occurring once has either an increasing subsequence of length five or a decreasing subsequence of length five

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