Tower of Hanoi

The Tower of Hanoi is a puzzle with a legend attached: monks in a distant temple are said to be moving 64 golden disks between pegs, and when the last disk falls into place, the world ends. The good news for everyone is that 64 disks need more than 18 quintillion moves, so the end is not near. Your version is more merciful — a stack of coloured disks, three pegs, and one iron rule: a larger disk may never rest on top of a smaller one.

You choose the challenge, from 3 disks up to 7. The catch is exponential: the perfect solution takes 2ⁿ − 1 moves, so 3 disks need just 7 moves, 5 disks need 31, and the full 7-disk tower needs a flawless 127. Your move counter runs beside the perfect figure the whole game, turning every solve into a personal efficiency contest — finishing in 40 moves on a 5-disk tower is a win, but it begs the question of where the 9 spare moves went.

The puzzle's real gift is the pattern it teaches. The solution is recursive: to move a tower of n disks, move the top n−1 out of the way, move the biggest disk once, then rebuild. Once you feel that rhythm — and the smaller secret that the smallest disk moves on every second turn, always in the same rotational direction — the tower stops being a maze and becomes a dance you can perform at any size.