### APMO 2017 P1

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**Sat May 27, 2017 1:07 pm**We call a $5$-tuple of integers arrangeable if its elements can be labeled $a, b, c, d, e$ in some order so that $a-b+c-d+e = 29$. Determine all $2017$-tuples of integers $n_1,n_2,...,n_{2017}$ such that if we place them in a circle in clockwise order, then any $5$-tuple of numbers in consecutive positions on the circle is arrangeable.