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edge of a cube, distances from a plane (V Soros Olympiad 1998-99 Round 2 11.5)

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May 25, 2024
geometry3D geometry

Problem Statement

It is known that the distances from all the vertices of a cube and the centers of its faces to a certain plane (1414 values in total) take two different values. The smallest is 11. What can the edge of a cube be equal to?