You have three small poles and five hoops - XS, S, M, L, XL (as in extra small, small, medium, large and extra large). They are placed on pole 1 in order, with largest at the bottom.

You can move one hoop at a time, and the hoops you are not moving have to be on a pole. You also cannot place a hoop on top of a smaller one. How can you move the hoops so that they are in the same order as they are now, but on pole 3?

In this classic tower of Babel problem, the clue to controlling the final position of the hoops is noticing the odd and even hoops. That is to say, begin by numbering the hoops from smallest to largest. If you want to move the tower of hoops to pole three you must begin by moving hoop #1 to pole three. Thereafter all even numbered hoops will first be moved to pole two, covered with their succesively smaller hoops until pole three is empty and available for the next larger odd numbered hoop. This, of course, applies to all tower sizes.

Posted by Eric on 2003-09-07 10:12:37