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March 28, 2017

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Mariolys is creating a numbered list of distinct integers. Luigis sees that there are N numbers in the list, and states that he can find either a subsequence of length 13 with increasing terms or a subsequence of length 17 with decreasing terms. What is the minimum value of N for Luigis' claim to be true?
Details and assumptions:
Luigis doesn't know the numbers on Mariolys list.

The chosen terms of the subsequence need not be consecutive. In the list {1,45,23,56,25,58,8,2}, we have an increasing subsequence of length 4 formed by 1,23,25,58 (which are the 1st, 3rd, 5th and 7th terms of the original list). We also have a decreasing subsequence of length 4 formed by 56,25,8,2 (which are the 4th, 5th, 7th and 9th terms of the original list).

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