Tower of Hanoi
About Tower of Hanoi
The Tower of Hanoi is one of the most elegant mathematical puzzles ever devised. You start with a stack of disks arranged by size on the leftmost peg, largest at the bottom. The goal: move the entire stack to the rightmost peg, one disk at a time, never placing a larger disk on top of a smaller one.
Why it trains your brain. The optimal solution for n disks requires exactly 2n - 1 moves, a fact that emerges naturally once you play enough. The puzzle forces recursive thinking: to move n disks to the right peg, you first move n-1 disks to the middle, move the bottom disk to the right, then move the n-1 stack on top. Players who internalize this pattern can solve it flawlessly every time.
Difficulty scales naturally. PlayMemorize starts you at 3 disks (7 moves minimum) and ramps up to 7 disks (127 moves minimum). A move budget above the optimal is given; the challenge tightens as your labyrinth level rises.
Part of the PlayMemorize family of brain-training games. Runs entirely in your browser, works offline as a Progressive Web App.
FAQ
Q: What is the minimum number of moves?
For n disks the minimum is exactly 2^n - 1 moves: 3 disks = 7 moves, 4 disks = 15, 5 disks = 31, 6 disks = 63, 7 disks = 127. PlayMemorize gives you a small budget above this minimum so beginners can still win while learning the pattern.
Q: How do I always find the optimal solution?
The recursive trick: to move n disks from A to C using B, first move n-1 disks from A to B, then move disk n from A to C, then move n-1 disks from B to C. Repeat this rule at every step and you will always reach the minimum move count.
Q: What happens if I run out of moves?
The round ends and is counted as a loss. You get to try again with a fresh puzzle. In the labyrinth, exhausting the move budget drops you back one level.
Q: Can I print Tower of Hanoi as a worksheet?
Yes. The worksheet version shows a sequence of peg-state diagrams and asks students to fill in the correct next move. Build a sheet from the master generator at /worksheets.
Q: Does it work offline?
Yes. PlayMemorize is a Progressive Web App. Install once and Tower of Hanoi plays anywhere without an internet connection.
