Tower of Hanoi Basics
📋 What it is
In Tower of Hanoi you move a stack of discs to another peg, one at a time, never putting a bigger disc on a smaller one.
🗣️ Coach says
The Tower of Hanoi looks tricky but hides a neat idea: to move a big stack, first move the top part out of the way, move the biggest disc, then move the top part back. Solving a big problem by solving a smaller copy of it — that’s recursion.
🧠 Memory hook
To move N discs: move the top N-1 aside, move the biggest, move the N-1 back.
😂 Giggle
Why did the puzzle enjoy the challenge?
Because it loved being figured out!
😲 Whoa!
A legend says monks are moving a 64-disc tower, and the world ends when they finish — but 64 discs need 18 quintillion moves, so we’re safe for about 585 billion years.
✅ Quick check: What’s the FEWEST moves to solve a 3-disc Tower of Hanoi?
Say your answer out loud first — then reveal.
7 moves — the pattern is 2^N − 1, and 2³ − 1 = 7.
Each extra disc roughly doubles the work, giving the 2^N − 1 formula.
🪄 Trick question: Does a 4-disc tower take 8 moves (just one more than 3)?
Careful — think it through, then reveal.
No — it takes 15 (2⁴ − 1); each disc DOUBLES the work plus one, it doesn’t just add one.
The move count grows exponentially (2^N − 1), not linearly.
🧪 Try it! (2 minutes)
Stack 3 different-size coins and solve it by hand, counting moves. Can you hit exactly 7?