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The Wisdom Ball (a.k.a. Mind Twister) is a ball that has 6 faces, each with a rotating cap with numbers from 1 to 8. Only the white cap has 7 numbers, leaving the 8th number with a gap where you can swap the tiles from one cap to another, thus allowing you to solve the puzzle.

You can make several challenges with it, like having each cap with its correspondent colored number, with a cw or ccw sequence. Watch out for parity problems. See Twistypuzzles.com on how to avoid this.