IMO 1984 LL MON36

The set {1, 2, . . ., 49} is divided into three subsets. Prove that

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IMO 1984 LL MON36

Origin: MON

Problem

The set {1, 2, . . ., 49} is divided into three subsets. Prove that at least one of these subsets contains three different numbers a, b, c such that a + b = c.