The Magnetic Tower of Hanoi (MToH) puzzle is a variation of the classical Tower of Hanoi puzzle (ToH), where each disk has two distinct sides, for example, with different colors "red" and "blue". The rules of the MToH puzzle are the same as the rules of the original puzzle, with the added constraints that each disk is flipped as it is moved, and that two disks may not be placed one on another if their touching sides have the same color. Each disk has a North and South pole, with similar poles repelling one another and opposite poles attracting one another. Magnets inside each disk physically prevent illegal moves.[1]
One of the striking features of the classical ToH puzzle is its relation to the base 2: the minimum number of total moves required to solve the puzzle is 2n − 1 (where n is the number of disks), while the minimum number of moves made by disk k is 2k − 1 (disks are numbered bottom up so that k = 1 being the largest disk, and k = n being the smallest). It will be shown below that just as the original ToH puzzle is related to base 2, so the MToH is related to base 3, though in a more complex manner.[2]
- ^ Cite error: The named reference
Levy2was invoked but never defined (see the help page). - ^ "Tower of Hanoi, the Hard Way". This is another variation of the ToH which relates to base 3.