May a person solve a rubik's cube on Shabbos?
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It would appear that it is permitted, see Shemiras Shabbas K'Hilchasa 16:24 which discusses a "two dimensional" puzzle where one rearranges the pieces which are attached to a frame and rules that it is permitted. It would seem that rubix cube is even easier to permit since there is no actual picture formed.
For what it is worth I think that it is an excellent question, because while none of them seem to quite fit, solving a rubix cube reminds us of a number of melachos.