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TOT 499 1996 Spring S A1 8 distances in a cube

Source:

August 16, 2024
geometry3D geometrycube

Problem Statement

Does there exist a cube in space such that the perpendiculars dropped from its eight vertices to a given plane are of length 0,1,2,3,4,5,60, 1, 2, 3, 4, 5, 6 and 77?
(V Proizvolov)
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