Tower of Hanoi with Three Disks
Lesson notes
Overview
Seven moves solve three disks. This topic is rated beginner and is number 79 of 117 in Computer Science. Core ideas and first intuitions. No prior knowledge needed.
What you are seeing
The panel above shows an interactive animation of the idea. Every slider changes one quantity so you can see its effect on the outcome. The animation is drawn live from the model, so everything you see responds to the sliders. Press Space to pause, use Restart to replay from the start, and change the speed to slow down quick events.
In depth
With three disks the recursive solution takes 2³ − 1 = 7 moves: move the top two disks to the spare peg in 3 moves, move the largest to the target peg in 1, and then move the two disks onto it in 3 more. Seeing the pattern with a small number helps in understanding the general recursion, where solving n disks reduces to solving n − 1 twice, and in proving that 2ⁿ − 1 is the minimum.
Reading the relationship
The expression "2³ − 1 = 7" is a compact summary of the idea. Then use the sliders to see how changing one quantity changes the others.
A guided exploration
1. Run the animation once with the default settings and describe in words what happens. 2. Change one slider at a time and note which quantity responds most. 3. Push each slider to its extreme and decide whether the result still makes sense.
Try this
Start by only moving one slider at a time. Say aloud what you expect, then check.
Common pitfalls
Test small inputs by hand and then the largest ones. Off-by-one errors and forgetting how cost grows with input size are the most common traps.
How it connects
It builds on “PageRank on a Larger Web”, the topic before it in Computer Science. Once you are comfortable, continue with “Tower of Hanoi with Six Disks”.
Why it matters
Computing ideas decide how fast, how safely and how well software can solve problems.
Where you might use it
- Revising “Tower of Hanoi with Three Disks” before a class, exam or certification
- Choosing the right algorithm or data structure when writing software or apps
- Debugging programs and judging how fast or how safely code will run at scale
- Understanding how search engines, games, phones and AI systems make decisions
Frequently asked questions
What is Tower of Hanoi with Three Disks?
Seven moves solve three disks. It is a beginner topic in Computer Science.
How do I use the Tower of Hanoi with Three Disks simulation?
The panel at the top shows an interactive animation of the idea. Every slider changes one quantity so you can see its effect on the outcome. Move the sliders one at a time, then press Space to pause the animation and look closer.
What does the formula mean?
The expression 2³ − 1 = 7 packs the idea into symbols. Name each symbol first, then change one quantity with the sliders and see which others respond.
Who is this topic for?
Core ideas and first intuitions. No prior knowledge needed. If the quiz feels hard, reread the lesson notes and try the previous topic first.
What should I learn before this?
Start with “PageRank on a Larger Web”, the previous topic in Computer Science. Each topic in a subject builds on the ones before it.
How do I track my progress?
Press “Mark as learned” on this page. Progress is stored only in this browser and is never sent anywhere. The Browse page can show topics you have learned or still need to learn.