axis parallel cubes combo geo
Source: 2020 Swedish Mathematical Competition p6
May 1, 2021
combinatorial geometrycombinatorics
Problem Statement
A finite set of axis parallel cubes in space has the property of each point of the room is located in a maximum of M different cubes. Show that you can divide the amount of cubes in subsets (or less) with the property that the cubes in each subset lacks common points. (An axis parallel cube is a cube whose edges are parallel to the coordinate axes.)