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The number of ``prime'' boxes is always finite, where a set of boxes is prime if it cannot be built up from one or more given configurations of boxes.
See also Conway Puzzle, Cuboid, de Bruijn's Theorem, Klarner's Theorem, Slothouber-Graatsma Puzzle
References
Honsberger, R. Mathematical Gems II. Washington, DC: Math. Assoc. Amer., p. 74, 1976.