Pole and minimum number of moves – math help needed
There are three poles in front of you. One pole is stacked with 64 rings ranging in weight from one ounce (at the top) to 64 ounces (at the bottom). Your task is to move all of the rings to one of the other to poles so that they end up in the same order. The rules are that you can only move one ring at a time, you can move a ring only from one pole to another, and you cannot even temporarily place a ring on top of a lighter ring.
What is the minimum number of moves you need to make to achieve the task?
Show a detailed proof and give a thorough explanation please.