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SE-SKOLORNAS 2020 Problem 6

    A finite set of axis parallelcubes 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 8(M−1)+18 (M - 1) + 1 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.)

    Dataset text AI-MO AoPS. Quoted with source.

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