The Tower of Hanoi

1. The Tower of Hanoi In the temple of Banares, says he, beneath the dome which marks the centre of the World, rests a brass plate in which are placed 3 diamond needles, each a cubit high and as thick as the body of a bee. On one of these needles, at the creation, god placed 64 discs of pure gold, the largest disc resting onthe brass plate and the others getting smaller and smallerupto the top one. This is the tower of brahma. Day and nightunceasingly the priests transfer the discs from one diamondneedle to another according to the fixed and immutable laws of brahma, which require that the priest on duty must not move more than one disc at a time and that he must place this disc on a needle so that there is no smaller disc below it. When the 64 discs shall have been thus transferred from the needle on which at the creation god placed them to one of the other needles, tower, temple and Brahmans alike will crumble into dust and with a thunder clap the world will vanish. Edouard Lucas (1884) Probably

2. Illegal Move The Tower of Hanoi 5 Tower A B C

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12. Investigation The Tower of Hanoi • Confirm that you can move a 3 tower to another peg in a minimum of 7 moves. • Investigate the minimum number of moves required to move different sized towers to another peg. • Try to devise a recording system that helps you keep track of the position of the discs in each tower. • Try to get a feel for how the individual discs move. A good way to start is to learn how to move a 3 tower from any peg to another of your choice in the minimum number of 7 moves. • Record moves for each tower, tabulate results look for patterns make predictions (conjecture) about the minimum number of moves for larger towers, 8, 9, 10,……64 discs. Justification is needed. • How many moves for n disks?

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