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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 the 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.〔 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 2''n'' − 1 (where ''n'' is the number of disks), while the minimum number of moves made by disk ''k'' is 2''k'' − 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.〔(【引用サイトリンク】url=http://www.cut-the-knot.org/recurrence/LongHanoi.shtml )〕 == Origin == Mathematically equivalent puzzles to certain variations of the MToH have been known for some time. For example, an equivalent puzzle to one of the colored variations of the MToH appears in Concrete Mathematics. In this puzzle moves are only allowed between certain posts, which is equivalent to assigning permanent colors to the posts (e.g. if two posts have the same permanent color assigned to them, then direct moves are not allowed between the two posts). The free (non-colored) MToH first appeared publicly on the internet〔(【引用サイトリンク】first=Fred )〕 around 2000 (though under the name of "Domino Hanoi") as part of a detailed review by the Mathematician Fred Lunnon of the different variations of the original Tower of Hanoi puzzle. The MToH was independently invented by the Physicist Uri Levy in the summer of 1984, who also coined the name and the analogy to magnetism. Dr Levy later published a series of papers dealing with the mathematical aspects of the MToH. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Magnetic Tower of Hanoi」の詳細全文を読む スポンサード リンク
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