May a person solve a rubik's cube on Shabbos?
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.
I saw from the link below that it is allowed, but for Adults it is not the Sabbath honour that the adults will play (note if it's creating a picture by solving the cube that is something else)
but somewhere else I saw this might be Borer
As we have shown, there are a few reasons to assume that Borer would apply to the Rubik’s Cube, and thus, since it may infringe on a Torah prohibition, adults should refrain from playing with it. This too was the ruling of HaRav Shlomo Miller שליט”א. As for children, while there is room to be lenient if necessary, it would obviously be proper Hinuch to avoid it.