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Interior of one of the regions meets at least three faces

Source: IMO LongList 1982 - P20

March 18, 2011
geometry3D geometrycombinatorics proposedcombinatorics

Problem Statement

Consider a cube CC and two planes σ,τ\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.
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