I first heard a similar idea from Reed Bowman (a metalworker, not a mathematician) last September. He proposed it instead on a 4x4x4 cube, in which each of the six faces and each of the twelve bands going around the cube (consisting of four squares from each of four faces) had to contain all sixteed numbers. Ed Pegg's Dec 4 update points to Steve Schaefer's (doubtless independent) implementation of the same geometry. Reed's idea was to put the starting position on a size-4 Rubik's cube in such a way that it was not solvable, and the challenge was to perform some small number of Rubik moves to convert it to a solvable initial position, and then solve it. Yow. --Michael On 12/21/05, Dave Dyer <ddyer@real-me.net> wrote:
Combine puzzle genres; Start with sudoku designed to be etched onto 6 faces of a cube (with common numbers in all the edge positions of adjacent faces. Now move the whole pattern to a rubik's cube, so each cubie corresponds to a 3x3 sudoku cell.
How likely are random positions of the rubik's puzzle to also be solvable as sudoku?
My guess: not very likely, but probably very difficult to prove that only the intended solved rubik's state is also solvable as sudoku.
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