About Tower of Hanoi
The Tower of Hanoi was invented by the French mathematician Édouard Lucas and sold as a toy in 1883, with a story about monks moving a tower of sixty-four golden discs. The rules are simple: move one disc at a time and never put a disc on a smaller one. On three pegs a tower of n discs takes 2 to the power of n, minus 1, moves, so three discs take 7 and six take 63. This page has seven puzzles, including a tower that starts spread over the pegs and two with a fourth peg, where the fewest moves are much harder to find.
How to play Tower of Hanoi
- Tap a peg to lift its top disc, then tap the peg to put it on. Tap the same peg again to put the disc back.
- Only one disc moves at a time, and a disc can never go on top of a smaller one.
- Build the whole tower on the right peg, marked with a star. Some puzzles have four pegs, and one starts with the discs spread out.
- The fewest possible moves earn three stars. Your progress is saved on this device only.
Tips & strategy
- Watch the smallest disc: in the fastest solution it moves on every other turn, always around the pegs in the same direction.
- To move a tower of five, first move the four on top out of the way, then the biggest disc, then the four back on top of it.
- With an odd number of discs the smallest disc goes straight to the target peg first; with an even number it goes to the middle peg.
- With four pegs, park a small tower on one spare peg, move the rest using the other pegs, then bring the small tower back.
Tower of Hanoi: questions and answers
How many moves does the Tower of Hanoi take?
On three pegs, a tower of n discs takes at least 2 to the power of n, minus 1, moves: 7 for three discs, 15 for four, 31 for five and 63 for six. A fourth peg saves a lot: 13 moves for five discs and 33 for eight.
Why is it called the Tower of Hanoi?
Its inventor, Édouard Lucas, sold it in 1883 with a made-up legend about a temple where monks move a tower of 64 golden discs. The name was part of the story.
Is my progress saved?
Yes, in your browser on this device: the puzzles you have solved, your stars and your best result for each.