CT102:
Towers of Hanoï
Taken From W.W. Rouse Ball & H.S.M. Coxeter,
Mathematical Recreations and Essays, 12th edition. Univ. of Toronto Press,
1974.
The De Parville account of the origen from La Nature,
Paris, 1884, part I, pp. 285-286.
"In the great temple at Benares beneath the dome that marks the centre of the world, rests a brass plate in which are
fixed three diamond needles, each a cubit high and as thick as the body of a bee. On one of these needles, at the
creation, God place sixty-four discs of pure gold, the largest disk resting on the brass plate, and the others getting
smaller and smaller up to the top one. This is the tower of Bramah. Day and night unceasingly the priest transfer the
discs from one diamond needle to another according to the fixed and immutable laws of Bramah, 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 sixty-four discs shall have been thus transferred from the needle which at creation
God placed them to one of the other needles, tower, temple, and Brahmins alike will crumble into dust and with a
thunderclap the world will vanish."
The number of separate transfers of single discs which the Brahmins must make to effect the transfer of the tower is
two raised to the sixty-fourth power minus 1 or 18,446,744,073,709,551,615 moves. Even if the priests move one disk
every second, it would take more than 500 billion years to relocate the initial tower of 64 disks.
Michael Mc Gettrick