A cutaway engine cylinder shows the piston, valves and spark through the four strokes of the cycle. Students change engine speed and spark advance and watch the stroke, cycle angle, cylinder pressure and valve states update.
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Tower of Hanoi
About this simulation
This simulation shows the classic Tower of Hanoi puzzle being solved by a recursive algorithm. Students choose from three to eight discs and watch one disc move at a time without ever placing a larger disc on a smaller one. Readouts show the moves made, the minimum number of moves, which is 2 to the power n minus 1, and the current move. A restart button begins again, and the main speed slider changes the pace. It is a vivid way to teach recursion and exponential growth in computing and maths lessons.
What students can explore
- Start with 3 Discs and count the moves, then check the Minimum readout.
- Add one disc at a time up to 8 and write down how the minimum doubles and then adds one.
- Press Restart and watch how the largest disc moves only once.
- Slow the main Speed slider and say aloud which sub-problem each move belongs to.
- Predict the minimum for 6 Discs before looking at the readout.
Learning objectives
- 1Describe the recursive strategy for solving the Tower of Hanoi.
- 2Calculate the minimum number of moves as 2 to the power n minus 1.
- 3Explain why the number of moves doubles with each extra disc.
- 4Use a pattern in a table of results to make a prediction.
Questions teachers ask
Is it free to use?
Yes. It is free to use in any modern browser, including whiteboards and tablets, and there is no sign-up.
What are the rules of the puzzle?
Move one disc at a time from one peg to another, and never place a larger disc on top of a smaller one. The goal is to move the whole stack from the first peg to the last.
How many moves does it take?
The minimum for n discs is 2 to the power n minus 1. That is 7 moves for 3 discs, 31 for 5 and 255 for 8, and the number roughly doubles every time you add a disc.
How do I use the Tower of Hanoi simulation?
Choose the number of Discs, press Restart, and watch the solver. Use the Speed slider to go faster or slower and compare the Moves made with the Minimum.
Embed this simulation
Drop it into your LMS, blog, or class site — free.
<iframe src="https://kiwibee.io/en/simulations/tower-of-hanoi-3d-simulation/embed" title="Tower of Hanoi | KiwiBee" loading="lazy" allowfullscreen style="width:100%;height:min(70vh,620px);min-height:420px;border:0;border-radius:16px"></iframe>Continue exploring
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