IMO 1992 LL CAN6

Origin: CAN

Problem

Suppose that n numbers x1, x2, . . . , xn are chosen randomly from the set {1, 2, 3, 4, 5}. Prove that the probability that x2 1 + x2 2 + \cdot \cdot \cdot + x2 n \equiv0 (mod 5) is at least 1/5.