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Flat Cube puzzle shown to require at least 27 moves to solve worst-case scramble
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A mathematical analysis of a 2D Rubik's Cube-like puzzle called the Flat Cube establishes a lower bound of 27 for God's number, the maximum moves needed to solve the most adversarial scramble, by mapping lozenge tilings to 3D cube arrangements.
This is a recreational mathematics result with no direct engineering consequence, carried by a single source with no corroboration. The technique of mapping a 2D tiling problem to a 3D packing problem is a notable combinatorial argument, but the practical relevance for software builders is minimal.
Written by elseif from the cluster below · every claim links back to a sourceThe three things worth knowing
The Flat Cube is a 2D puzzle of rhombus-shaped lozenges where three lozenges forming a hexagon can be twisted together by multiples of 60 degrees.
God's number for the Flat Cube is shown to be at least 27, compared to 20 for the standard Rubik's Cube when a 180-degree twist counts as one move.
The proof maps each lozenge tiling to a configuration of unit cubes in a 3-by-3-by-3 tray, where each twist adds or removes exactly one cube, so an empty-to-full transition requires 27 moves.
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