Tower of Hanoi· Advanced

Goal

Move all disks from the first peg to the third peg.

How to Play

  • Tap a peg to pick up the top disk.
  • Tap another peg to place the disk there.
  • Tap the same peg again to cancel the selection.

Rule 1: One Disk at a Time

You can only move one disk at a time. You cannot move multiple disks together.

OK
NG

Rule 2: Larger Cannot Go On Smaller

A larger disk cannot be placed on top of a smaller disk. Smaller disks must always be on top.

OK
NG

Completed Example

  • Only one disk can be moved at a time.
  • A larger disk cannot be placed on top of a smaller disk.
  • Tap a peg to select a disk, then tap another peg to move it.
ABC

Tip

  • Plan a strategy to move the largest disk to the target peg first.
  • For an odd number of disks, move the first disk to the target peg; for even, to the auxiliary peg.
  • The minimum number of moves is 2^n - 1. Thinking recursively will help you find the optimal solution.

The Tower of Hanoi, invented by French mathematician Édouard Lucas in 1883, is used as a standard tool in neuropsychology for assessing planning ability and executive function.

  • Welsh & Huizinga (2001) - Tower of Hanoi and frontal lobe function
  • Goel & Grafman (1995) - Neuroimaging study of Tower of Hanoi and planning