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Arithmetic Sequence in Every Intersection

Source: Turkey TST 2016 P7

April 10, 2016
arithmetic sequencecombinatorics

Problem Statement

A1,A2,…AkA_1, A_2,\dots A_k are different subsets of the set {1,2,…,2016}\{1,2,\dots ,2016\}. If Ai∩AjA_i\cap A_j forms an arithmetic sequence for all 1≤i<j≤k1\le i <j\le k, what is the maximum value of kk?
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