IMO 1986 LL GDR37

Prove that the set {1, 2, . . ., 1986} can be partitioned into 27

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IMO 1986 LL GDR37

Origin: GDR

Problem

Prove that the set {1, 2, . . ., 1986} can be partitioned into 27 disjoint sets so that no one of these sets contains an arithmetic triple (i.e., three distinct numbers in an arithmetic progression).