How to play Disc Towers
Move a stack of discs to the last peg, one at a time, never putting a bigger disc on a smaller one. Also known as Tower of Hanoi.
The rules
- There are three pegs, A, B and C. The discs start on the pegs, biggest at the bottom.
- Move one disc at a time: the top disc of one peg onto another peg.
- A disc may never be placed on a smaller disc.
- Get every disc onto peg C. In the neighbours-only rules, a disc may only move to the next peg along.
Playing Disc Towers on Puzzle Solvers
- Choose how many discs (3 to 7) and the rules — classic, neighbours only, or a scrambled start — then press New Puzzle.
- Tap a peg to pick up its top disc, then tap another peg to put it down. Keys A, B and C work too.
- A disc may never sit on a smaller disc. Move the whole stack to peg C.
- Hint shows the best next move and explains the plan behind it.
A worked example
Three discs on A. The big disc must go to C, so the two smaller discs must first be stacked on B.
To move two discs to B: small to C, middle to B, small onto B. Now the big disc moves to C, and the two discs follow the same pattern from B to C — seven moves in all.
Strategies
- Biggest disc first. Find the biggest disc not yet in place. Everything smaller must be stacked on the spare peg before it can move.
- A smaller copy. Moving n discs = move n − 1 discs out of the way, move the biggest, move the n − 1 back on top.
- The smallest disc cycles. In the classic rules, the smallest disc moves every other turn, always round the pegs in the same direction.
- Count the moves. With n discs the fewest moves is 2ⁿ − 1: 7 for three discs, 31 for five, 127 for seven.
Common mistakes
- Moving the smallest disc to the wrong peg at the start — with an odd number of discs it goes straight to the target peg.
- Losing track of the plan and undoing earlier work.
Where it comes from
The puzzle was published by the French mathematician Édouard Lucas in 1883, with a legend about monks moving 64 golden discs. It is a favourite example of recursion in mathematics and computing.
Frequently asked questions
What is the fewest number of moves?
For the classic start, 2ⁿ − 1 moves for n discs. The counter shows the fewest for your position.
What are the neighbours-only rules?
A disc can only move between neighbouring pegs (A↔B, B↔C), never straight from A to C. It takes many more moves.
Can I undo?
Yes — Undo and Redo work for every move.
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