Teach 180: The Tower of Hanoi (Day 165)

There are certain math ideas or puzzles that I believe every student should experience. The Tower of Hanoi is one of those puzzles.  After we reviewed the graphs of the six basic trig functions in Calculus today, we had some time to play with this puzzle.  Our goal was to move the disks from the left peg to the right peg in as few moves as possible.  The rule is that you can't place a larger disk on top of a smaller disk.  Rather than starting with 7 disks, we started with 1 and then moved to 2 and then 3, looking for a pattern as we increased the number of disks.  It only took about 10 minutes to see that the number of moves, M, based on the number of disks D, is given by the function M(D) = 2D - 1.

If you are looking for an animation of the tower of Hanoi, there is a nice 2-D and 3-D simulation at Towers of Hanoi Animation.  I will probably show this tomorrow and we may even create a pop-up card based on the towers of Hanoi.