Imagine that you have access to an infinite number of n-dimensional cubes and an infinite amount of time. Each cube is made by a particular artist and each cube is made using a particular material. What is the smallest number of different materials required to fill an infinite n-dimensional space with cubes if there are no more artists than materials, each artist can work with any material, two n-dimensional cubes of the same material or made by the same artist may not share an (n-1)-dimensional side, and two n-dimensional cubes of the same material that are also made by the same artist may not share an (n-2)-dimensional side?
I haven't solved this for the general case myself, but I posted it to rec.puzzles November 12th 2001. When I have a solution I may put a link to it from this page.
Back to puzzles and brain teasers© 2001 Andreas Gunnarsson
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