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Tower of Hanoi: one disk at a time.

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Move the whole tower to the goal peg. Only one disk moves at a time, and no disk may sit on a smaller one. Find the fewest moves, then try scrambled towers and extra pegs.

3 tiers · 24 levels: Classic → Mid-game → Variants
Ages 7+
3–30 min
🔊 Sound
logic
recursion
planning
Free · no sign-up

How to play Tower of Hanoi

Tap a peg to lift its top disk, then tap the peg you want to drop it on. On a keyboard, press 1, 2, 3 (and 4, 5).
A disk can only go on an empty peg or on a bigger disk.
Build the whole tower on the peg marked GOAL. The game shows the best possible number of moves.
Stuck? A hint shows a perfect next move (it costs a star). 🤖 Show me plays the perfect solution.
Tier 2 starts from scrambled positions; tier 3 allows only next-door moves, or adds a fourth and fifth peg.

Tips and strategy

With an odd number of disks, move the smallest disk to the goal peg first; with an even number, to the other peg.
The smallest disk moves every other turn, always going round the pegs in the same direction.
To move n disks, first move the top n − 1 out of the way, move the biggest, then move the n − 1 back on top. That idea is called recursion.
The best number of moves for n disks is 2ⁿ − 1: 7 for 3 disks, 15 for 4, 31 for 5, 63 for 6, 127 for 7.

What you'll learn

The Tower of Hanoi is a classic logic puzzle with three pegs and a stack of disks. Move the complete stack to another peg, one disk at a time, without ever placing a larger disk on a smaller one. The puzzle was introduced by French mathematician Édouard Lucas in 1883 and is still used to teach planning, powers of two and recursion.

Tower of Hanoi rules

Move only one disk on each turn.
Lift only the top disk from a peg.
Place a disk on an empty peg or on a larger disk.
Finish with every disk stacked in the right order on the goal peg.

Minimum moves for 1 to 8 disks

For the standard puzzle with three pegs, the minimum number of moves for n disks is 2ⁿ − 1. Each extra disk nearly doubles the number of moves:

1 disk: 1 move · 2 disks: 3 moves · 3 disks: 7 moves
4 disks: 15 moves · 5 disks: 31 moves · 6 disks: 63 moves
7 disks: 127 moves · 8 disks: 255 moves

For example, the three-disk solution takes seven moves: move the small disk to the goal, the medium disk to the spare peg, the small disk onto the medium disk, the largest disk to the goal, then move the two smaller disks onto it.

Why is Hanoi a recursion puzzle?

To move n disks, first move the top n − 1 disks out of the way, move the largest disk once, then move those n − 1 disks onto it. The same smaller problem happens twice, so the move count follows M(n) = 2M(n − 1) + 1. That is recursion: solving a problem by using smaller copies of the same problem. Programmers use this idea in algorithms, and students can explore the number pattern in our powers of two lesson and Python coding adventure.

Four-peg and neighbour-move variants

The formula 2ⁿ − 1 applies to the classic three-peg puzzle. An extra peg changes the best strategy: in the four-peg version, eight disks can be solved in 33 moves. Neighbour-only versions also have different move counts. Try these variations in the game after learning the classic pattern.

Play more free logic and puzzle games, or read our step-by-step Tower of Hanoi solution guide for the full algorithm and examples.

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FAQ

Tower of Hanoi: questions

What is the minimum number of moves for the Tower of Hanoi?

For n disks and three pegs, the fewest moves is 2ⁿ − 1: 7 moves for 3 disks, 15 for 4, 31 for 5, 63 for 6, 127 for 7 and 255 for 8.

How do you solve the Tower of Hanoi with three disks?

It takes at least seven moves. Move the smallest disk to the goal, move the middle disk to the spare peg, put the small disk on the middle disk, move the largest disk to the goal, then move the two smaller disks onto the largest disk.

What is the trick to solving the Tower of Hanoi?

Move the smallest disk every other turn, always round the pegs in the same direction, and in between make the only other legal move. Or think recursively: move the top n − 1 disks aside, move the largest disk, then move the n − 1 disks back on top.

What does the Tower of Hanoi teach in computer science?

It is a visual way to understand recursion, base cases and algorithms. A program can solve n disks by solving the n − 1 disk puzzle twice, with one move of the largest disk between them.

How does the four-peg version change things?

An extra peg gives more room, so far fewer moves are needed: 8 disks take 255 moves on three pegs but only 33 on four.

Is the Tower of Hanoi good for kids?

Yes. With 3 disks it suits children from about 7; larger towers build planning, patience and pattern spotting, and older students can explore the maths of recursion.

Is it free?

Yes. No sign-up or ads, and your stars are saved in your browser.

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