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Rolling 1x1x1 cube on a 8x8 board with one face outside.

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February 12, 2011
geometry3D geometrycombinatorics unsolvedcombinatorics

Problem Statement

A 1×1×11\times 1\times 1 cube is placed on an 8×88\times 8 chessboard so that its bottom face coincides with a square of the chessboard. The cube rolls over a bottom edge so that the adjacent face now lands on the chessboard. In this way, the cube rolls around the chessboard, landing on each square at least once. Is it possible that a particular face of the cube never lands on the chessboard?
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