Cut the knot: learn to enjoy mathematics
A math books store at a unique math study site. Learn to enjoy mathematics.
Terms of use
Privacy Policy

More Mathematics
CTK Exchange

Games to Relax
Guest book
Recommend this site

Sites for teachers
Sites for parents

Manifesto: what CTK is about Buying a book is a commitment to learning Things you can find on CTK Email to Cut The Knot Recommend this page

3-Colors Tower of Hanoi

Professor John Mason of the Open University alerted me to the fact that the 3-color Tower of Hanoi puzzle is solvable if the goal is to affect a derangement of stacks of disks of the same color. The only restriction for a move is that a bigger disk can't be placed on top of a smaller one.

(To work out the puzzle, drag the disks from one peg to another. Drop it there.)

<hr> <h3> This applet requires Sun's Java VM 2 which your browser may perceive as a popup. Which it is not. If you want to see the applet work, visit Sun's website at, download and install Java VM and enjoy the applet. </h3> <hr>

The puzzle is indeed solvable. You should not try it, though, if your patience is lacking. Time permitting I'll add an animated solution.

Stuart Anderson came up with a recursive algorithm for automatic solution of the puzzle. You can see how it works either Slow or Fast

Copyright © 1996-2008 Alexander Bogomolny