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The Tower of Hanoi (also called The problem of Benares Temple [1] or Tower of Brahma or Lucas' Tower [2] and sometimes pluralized as Towers, or simply pyramid puzzle [3]) is a mathematical game or puzzle consisting of three rods and a number of disks of various diameters, which can slide onto any rod.
[1] [2] Each state of the puzzle is determined by the choice of one tower for each disk, so the graph has vertices. [2] In the moves of the puzzle, the smallest disk on one tower is moved either to an unoccupied tower or to a tower whose smallest disk is larger.
The puzzle consists of a gray base that resembles a city skyline, plus 36 colored towers. The towers come in six different colors and six different heights. The goal of the puzzle is to place all the towers onto the base so as to form a level cube with each of the six colors appearing once, and only once, in each row and column.
A solution is optimal if the sequence of moves is as short as possible. The highest value of this, among all initial configurations, is known as God's number, [3] or, more formally, the minimax value. [4] God's algorithm, then, for a given puzzle, is an algorithm that solves the puzzle and produces only optimal solutions.
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 ...
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He found an elegant binary solution to the Baguenaudier puzzle. [7] He also invented the Tower of Hanoi puzzle in 1883, which he marketed under the nickname N. Claus de Siam, an anagram of Lucas d'Amiens, and published for the first time a description of the dots and boxes game in 1889. Lucas died in unusual circumstances.
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