This question is bugging me for a long while:
Is it possible to turn an unmodified 3x3x3 Rubik's Cube into a position where there is a Glider pattern (from Conway's Life) on every side of the cube?
How many different solutions are there if we only care of the relative position of the gliders but not their colors? What are these?
(Being unmodified is important because it is possible to disassemble and then reassemble a cube so that it can't be solved again with standard turning moves. So reassembling a cube to a form matching my requirements doesn't count as a solution in itself.)
My Rubik's cube says it's possible: