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Vertices of a cube - Iran NMO 2007 - Problem2

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September 22, 2010
geometry3D geometrycombinatorics unsolvedcombinatorics

Problem Statement

Two vertices of a cube are A,OA,O such that AOAO is the diagonal of one its faces. A n−n-run is a sequence of n+1n+1 vertices of the cube such that each 22 consecutive vertices in the sequence are 22 ends of one side of the cube. Is the 1386−1386-runs from OO to itself less than 1386−1386-runs from OO to AA or more than it?
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