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?
This is the easiest solution I know:
* On odd turns, move the smallest hoop clockwise.
* On even turns, make the only possible move that doesn't involve the smallest hoop.
Depending on how many hoops there are, and which is your "target" pole, the first rule may read "anti-clockwise"; details left to the reader ;-)
A non-recursive solution
