Allen Walton

The Tower of Hanoi Puzzle

Long ago, there was a myth dealing with a challenging puzzle. Legend has it that a Hindu temple was bound to fall if young priests could ever solve this problem. Supposedly, these monks started this puzzle very long ago and when they solved it, the entire universe would, poof, be gone. But, their dilemna was one that would seem to take an eternity to solve.

This legend became a puzzle and a game in the late 1800's. A French mathematician had heard the myth and decided to build himself a game.

The Pieces of the Game:

You are given three poles with a number of disks on one. The largest disk is the one on the bottom and every time you go one up, the disks become smaller. Therefore, the smallest disk is on top.

Rules of the Game:

The object of the game is to successfully move the stack of disks from one pole to another. The stack must be in the same order, meaning the largest one on the bottom and the smallest on top. When moving pieces, you can not place any disk on top of a smaller disk. If one disk is bigger than another, it must be below it. The goal is to take the least moves possible to transfer all the disks.

Now, if you think you are ready for the challenge, click here to play the game. Set the number of disks according to how comfortable you are with the rules of the game.

After trying the game out, do you have any ideas about a formula for how many moves it takes? Let's look at a chart:

 The Number of Disks The Number of Moves 1 1 2 3 3 7

OK, so now you see a pattern? No, well try the next few higher possibilities. If you don't start to see one, try this equation: 2^n - 1. Plug in the number of disks for n and see what you get. Does that seem to work? It should.

Well, now you are already becoming a master at the game. I challenge you to go as high as you can and do it in the fewest moves. GOOD LUCK!!!!!