IMO 1982 LL CZS20

Consider a cube C and two planes \sigma, \tau, which divide Euclidean

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IMO 1982 LL CZS20

Origin: CZS

Problem

Consider a cube C and two planes \sigma, \tau, which divide Euclidean space into several regions. Prove that the interior of at least one of these regions meets at least three faces of the cube.