Tower of Hanoi

French mathematician Edouard Lucas introduced the Tower of Hanoi in 1883 as a mathematical puzzle wrapped in a legend about monks moving 64 golden disks. According to the story, the monks must transfer the disks between three pegs following strict rules, and when they finish, the world ends. At one move per second, solving 64 disks takes roughly 585 billion years. The puzzle challenges you to move a stack of disks from one peg to another, moving one disk at a time and never placing a larger disk on a smaller one. The minimum number of moves follows the formula 2^n - 1, where n is the number of disks. Three disks take 7 moves. Eight disks take 255. Play our browser version right now and see how close you can get to the optimal count.

1. Choose a disk count from 3 to 10. More disks mean a longer and harder puzzle.
2. Click a peg to pick up its top disk. The selected disk floats above the peg.
3. Click a second peg to place the disk. The game rejects any move that puts a larger disk on a smaller one.
4. Use the 1, 2, and 3 keys on your keyboard to select pegs A, B, and C without using the mouse.
5. Move every disk from peg A to peg C. The game tracks your move count and compares it to the optimal solution.
6. Press the Auto-Solve button at any time to watch the recursive algorithm solve the puzzle step by step.

• Move exactly one disk at a time.
• Only the top disk of any peg can be picked up.
• A larger disk can never sit on top of a smaller disk.
• The goal is to transfer the entire stack from peg A to peg C.
• You can use peg B as a temporary holding peg during the transfer.
• The puzzle always has a solution, and the minimum move count equals 2^n - 1.

• Think recursively. To move n disks from A to C, first move n-1 disks from A to B, move the largest disk from A to C, then move n-1 disks from B to C. This is the exact algorithm the auto-solver uses.
• Focus on the bottom disk first. Before you can move the largest disk to peg C, every other disk must sit on peg B in correct order.
• Track the parity of your moves. For an odd number of disks, the smallest disk cycles A, C, B, A, C, B. For an even number, it cycles A, B, C, A, B, C. Following this cycle guarantees an optimal solution.
• Avoid backtracking. If you move a disk and immediately move it back, you waste two moves. Every move should advance the puzzle toward the goal.
• Start with 3 disks to learn the pattern. Once you can solve 3 disks in 7 moves, scale up one disk at a time. Each additional disk roughly doubles the required moves.

• Classic (3 pegs): The standard version with three pegs. The minimum solution requires 2^n - 1 moves.
• Reve's Puzzle (4 pegs): Uses four pegs instead of three. The Frame-Stewart algorithm solves it in fewer moves than the classic version, making it a popular variant in computer science courses.
• Bicolor Tower of Hanoi: Disks come in two colors. You must separate the colors so each peg holds only one color, adding a sorting constraint on top of the size rule.

• The rules take 30 seconds to learn but the puzzle scales to real mathematical complexity.
• Every disk count has a known optimal solution, so you always have a target to beat.
• The recursive pattern teaches algorithmic thinking in a hands-on way.
• Games finish quickly. Three disks take under a minute, and even ten disks can be solved in under 20 minutes.

Play Tower of Hanoi free in your browser. Choose 3 to 10 disks, click pegs to move disks, and track your move count against the optimal solution. Use the auto-solver to watch the recursive algorithm in action. The game saves your best move count per disk size locally. No downloads, no registration, works on desktop and mobile.

Tower of Hanoi pairs simple rules with deep mathematical structure. Whether you solve 3 disks in seconds or tackle 10 disks for a real challenge, every game teaches you something about recursion. Pick your disk count and start moving.

• Edouard Lucas and the Tower of Hanoi - Mathematical Association of America
• The Tower of Hanoi - Myths and Maths - A. M. Hinz, S. Klavzar, U. Milutinovic, C. Petr