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APMO 2017: Arrangeable tuples

Source: APMO 2017, problem 1

May 14, 2017
combinatoricsAPMO

Problem Statement

We call a 55-tuple of integers arrangeable if its elements can be labeled a,b,c,d,ea, b, c, d, e in some order so that a−b+c−d+e=29a-b+c-d+e=29. Determine all 20172017-tuples of integers n1,n2,...,n2017n_1, n_2, . . . , n_{2017} such that if we place them in a circle in clockwise order, then any 55-tuple of numbers in consecutive positions on the circle is arrangeable.
Warut Suksompong, Thailand
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