towers of hanoi

Towers of Hanoi
Hanoi

   <games> A classic computer science problem, invented by
   Edouard Lucas in 1883, often used as an example of
   {recursion}.

   "In the great temple at Benares, says he, beneath the dome
   which 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 placed sixty-four discs of pure gold, the
   largest disc 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 priests
   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 on
   which at the 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 recursive solution is: Solve for n-1 discs recursively,
   then move the remaining largest disc to the free needle.

   Note that there is also a non-recursive solution: On
   odd-numbered moves, move the smallest sized disk clockwise.
   On even-numbered moves, make the single other move which is
   possible.

   ["Mathematical Recreations and Essays", W W R Ball, p. 304]

   The rec.puzzles Archive
   (http://rec-puzzles.org/sol.pl/induction/hanoi).

   (2003-07-13)