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rooks on surface of a 50x50x50 cube

Source: Saint Petersburg MO 2016 11.2

May 1, 2019
maxcubecombinatorics3-Dimensional Geometrycombinatorial geometrygeometry3D geometry

Problem Statement

The rook, standing on the surface of the checkered cube, beats the cells, located in the same row as well as on the continuations of this series through one or even several edges. (The picture shows an example for a 4×4×44 \times 4 \times 4 cube,visible cells that some beat the rook, shaded gray.) What is the largest number do not beat each other rooks can be placed on the surface of the cube 50×50×5050 \times 50 \times 50?
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