In the 1966 Doctor Who story The Celestial Toymaker, the eponymous villain forces the Doctor to play a ten-piece 1,023-move Tower of Hanoi game entitled The Trilogic Game with the pieces forming a pyramid shape when stacked.
(This story makes reference to the legend about the Buddhist monks playing the game until the end of the world.) The protagonist knows that a rescue ship might take a year or more to arrive, so he chooses to play Towers of Hanoi with 64 disks. In the science fiction story "Now Inhale", by Eric Frank Russell, a human is held prisoner on a planet where the local custom is to make the prisoner play a game until it is won or lost before his execution. The minimal number of moves required to solve a Tower of Hanoi puzzle is 2n − 1, where n is the number of disks.
With 3 disks, the puzzle can be solved in 7 moves. No disk may be placed on top of a smaller disk. Each move consists of taking the upper disk from one of the stacks and placing it on top of another stack or on an empty rod. The objective of the puzzle is to move the entire stack to another rod, obeying the following simple rules: The puzzle starts with the disks in a neat stack in ascending order of size on one rod, the smallest at the top, thus making a conical shape. It consists of three rods and a number of disks of different sizes, which can slide onto any rod. The Tower of Hanoi (also called the Tower of Brahma or Lucas' Tower and sometimes pluralized) is a mathematical game or puzzle.
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