Definition
Plain language
A classic puzzle where you move a stack of different-sized disks between three pegs, never putting a bigger disk on a smaller one.
As stated in the literature
A recursive planning benchmark with a known-optimal solution and a fully enumerable state space (3^n configurations for n disks), widely used to probe multi-step planning and state tracking in reasoning models.
Also called: Hanoi
Why it matters: Because its optimal solutions and full space of positions can be computed exactly, it lets researchers grade a model's multi-step planning against unambiguous ground truth.
For example, with three disks stacked largest-to-smallest on the left peg, you can move them all to the right peg in seven moves if you never place a larger disk on a smaller one.
Heard on the show
“A reasoning model builds a perfect internal map of the Tower of Hanoi before it writes a single word of its answer.”Episode 237 — The Model Built a Perfect Map of the Puzzle, Then Lost It