The Tower of Hanoi is a famous puzzle about patience and planning. Move the whole stack of discs from the first peg to the last, one disc at a time, never putting a bigger disc on a smaller one. Three discs take 7 moves; ten take 1,023. Stuck halfway? The solver finishes from wherever you are, in the fewest possible moves.
loading toolHow to play the Tower of Hanoi
- Choose how many discs (start with 3 or 4).
- Tap a peg to lift its top disc, then tap another peg to drop it.
- Move the whole tower to peg 3, never placing a bigger disc on a smaller one.
- Press “Show me the solution” to watch the fewest moves from your current position.
Good to know
- Keyboard: press 1, 2 or 3 to pick up and drop, or use the arrow keys and Enter.
- The smallest disc moves on every other turn, always in the same direction around the pegs.
Questions
What is the fewest number of moves?
For n discs it is 2ⁿ − 1: 3 discs need 7, 4 need 15, 5 need 31, 8 need 255 and 10 need 1,023.
What is the trick?
To move a tower of n discs, first move the top n − 1 discs out of the way, move the biggest disc, then move the n − 1 discs back on top of it. The same idea repeats for every smaller tower.
Why is it used in schools?
It is a classic way to teach recursion in computing and powers of two in maths, and a good test of planning ahead.
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