In the" Tower of Hanoi" we have a set of weights, all different (say Wo< W<<...< W,) divided at each position of the game into three piles (say a, b, c) any of which may be empty. The object of the game is to move all the weights from the end position A in which all the weights are on pile a, to the end position B in which all are on b, in the smallest number of moves subject to the following rules:(i) one weight may be moved at a time from one pile to another, if (ii) there are no smaller weights (than the one moved) either on the pile it comes from, or the pile it goes to (or, equivalently, all smaller weights must be on the third pile).