The Tower of Hanoi Math Game

One of my favorite math games as a kid was The Tower of Hanoi. I had no idea what it was called until college, though. To me it was another cheap wooden puzzle. Or a game you could play with four coins and 10 toothpicks.

The object of the game:

  • Move the stack from where it is, to another square or post.

The rules of the game:

  • You can only move one disk (or coin) at a time.
  • You can only put a disk (or coin) on top of one that’s bigger – physically. (I.e. you can’t put a big one on top of a smaller one.)

You can play it online for free (at a bazillion places, including below) or buy a physical version in classic or kid-friendly versions.

Here it is in a quick online version from

How can you use The Tower of Hanoi with your kids?

In the Tower of Hanoi puzzle, the math is vast – especially for such a simple little puzzle. But the math can be discovered gradually.

Present these challenges to your kids, one at a time:

  1. Move the stack according to the rules (just get it to another place.)
  2. Move the stack according to the rules in as few moves as possible. How many moves is that?
  3. Make the stack smaller or larger. Then move the stack according to the rules in as few moves as possible. How many moves is that?
  4. Repeat challenge #3 with many different numbers of coins/disks. Use cut out pieces of paper if necessary.
  5. Determine how many moves it would take to move a stack of 100 disks. Or 1000 disks.
  6. Then figure out a way to say this without numbers. In other words, create some sort of formula that will tell you how many moves you need to move any number of disks.

These challenges might range over many many years. I first learned of The Tower of Hanoi when I was about ten. And I’m still learning about it 30 years later.

Oh, and try to resist giving them any answers – ever. Instead let them work on it in their spare time.

Your turn!

Have you played The Tower of Hanoi math game, or a version of it? Do you remember the first time you came across it? Did you learn or teach math with it?

And how will you introduce it to your kids?

Share your thoughts in the comments!

Oh – and let others know about it on twitter…

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