Consider a cube on a table with each of the faces painted a different color. Suppose you were to pick up the cube, turn it around, then return it to its original position with the same colors permuted. Of the ways to reposition the cube, in how many cases does no color occupy its original position?
2026-03-25 13:42:15.1774446135
Ways to change a cube's position?
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In 14 of 24 cases. Only identity "rotation" and 9 rotations about the axes connecting the centers of the opposite faces leave some (6 or 2) colors on their original positions.