Trouble is, having thought for a few minutes, I've decided Rubik's Menger Sponge is probably straightforward to solve.
Consider M1. It consists of eight corners and twelve edges. The corners can be oriented as for a normal cube, but then the edge pieces, rather than being mutually distinct, are in four each of three different patterns. (I'm assuming an edge piece can spin freely about the axis between its adjacent corners.) The manipulations required to bring them into position are trivial compared with a traditional Rubik's Cube.
With M2, it gets a little less clear what degrees of freedom there are, but more equivalences and more degrees of freedom both help the solver.
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Date: 2009-06-13 03:26 pm (UTC)Consider M1. It consists of eight corners and twelve edges. The corners can be oriented as for a normal cube, but then the edge pieces, rather than being mutually distinct, are in four each of three different patterns. (I'm assuming an edge piece can spin freely about the axis between its adjacent corners.) The manipulations required to bring them into position are trivial compared with a traditional Rubik's Cube.
With M2, it gets a little less clear what degrees of freedom there are, but more equivalences and more degrees of freedom both help the solver.