Below is a concise “recipe” for solving any Tower of Hanoi problem, followed by resources for the specific 10-disk case.
Universal algorithm (recursive method)
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Label the pegs
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A = start (source) peg
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B = auxiliary (helper) peg
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C = goal (target) peg
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Recursive rule for n disks
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Move the top n − 1 disks from A to B (using C as helper).
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Move disk n (the largest remaining disk) from A to C.
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Move the n − 1 disks from B to C (using A as helper).
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Base case
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When n = 1, move that single disk straight from the source to the target.
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Move-count formula
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Minimum moves = 2ⁿ − 1.
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For 10 disks, that’s 1 023 moves.
Why it works
At every stage you treat the top stack of n − 1 disks as a single “meta-disk.”
Because disks must always stay in size order, you have no choice but to clear all of them off the largest disk before you can move that largest one; afterward you restack them. The recursion naturally produces the unique optimal sequence.
Working with 10 disks
| Disk | From → To | Pattern insight |
|---|---|---|
| 1 | Alternates every move | Smallest disk moves on every odd-numbered move. |
| 2 | Alternates every 2 moves | Disk 2 moves on every 2ⁿᵈ odd-numbered move. |
| … | … | … |
In practice, many people solve large instances by repeating three rules (for three-peg puzzles):
- Make the only legal move with the smallest disk.
- Make the only legal move that doesn’t involve the smallest disk.
- Repeat until complete.
Full 1 023-move walkthrough
I’ve generated the entire numbered move list for you and saved it as a plain-text file. You can open it in any editor or import it into a spreadsheet if you want to study patterns.Download the full 10-disk move list_Preview of the first 20 moves (source → target peg):_
pgsql
1: Move disk 1 from A to B 2: Move disk 2 from A to C 3: Move disk 1 from B to C 4: Move disk 3 from A to B 5: Move disk 1 from C to A 6: Move disk 2 from C to B 7: Move disk 1 from A to B 8: Move disk 4 from A to C 9: Move disk 1 from B to C 10: Move disk 2 from B to A 11: Move disk 1 from C to A 12: Move disk 3 from B to C 13: Move disk 1 from A to B 14: Move disk 2 from A to C 15: Move disk 1 from B to C 16: Move disk 5 from A to B 17: Move disk 1 from C to A 18: Move disk 2 from C to B 19: Move disk 1 from A to B 20: Move disk 3 from C to A