Tower of Hanoi
Move all discs from the left peg to the right peg. You can only place a smaller disc on a larger one.
0
Moves
7
Min Moves
-
Best Moves
Click a peg to select it, then click destination
About Tower of Hanoi
Tower of Hanoi is a classic mathematical puzzle invented in 1883. You have three pegs and a number of discs of different sizes stacked smallest-on-top on the leftmost peg. The goal is to move the entire stack to the rightmost peg in the minimum number of moves.
Controls
- Click a peg to pick up the top disc from that peg
- Click another peg to place the held disc there (only valid moves are allowed)
- Disc count buttons (3ā7) - choose how many discs to play with
- Reset button - restart the puzzle at any time
How to Play
- Move all discs from the left peg to the right peg.
- You may only move one disc at a time - always the topmost disc on any peg.
- A larger disc can never be placed on top of a smaller disc.
- The minimum number of moves to solve is 2āæ ā 1 (e.g., 7 moves for 3 discs, 31 for 5).
- Try to solve it in the minimum moves to get a perfect score!
Frequently Asked Questions
The minimum number of moves to solve n discs is 2^n ā 1. For 3 discs: 7 moves. For 4 discs: 15 moves. For 7 discs: 127 moves. The game tracks your move count.
Yes. The recursive pattern is: move the top nā1 discs to the auxiliary peg, move the largest disc to the destination, then move the nā1 discs from auxiliary to destination. Repeat recursively.
No. The only rule is that you cannot place a larger disc on top of a smaller disc. You can place smaller discs on larger ones, or onto empty pegs freely.
You can typically choose from 3 to 7 discs. Start with 3 for a quick puzzle (7 moves), or try 5ā7 discs for a more demanding challenge.