Cut the knot: learn to enjoy mathematics
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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

Looping Chips Puzzle

In this puzzle, 12 squares are arranged in a chain pattern with four chips of different colors covering the first four squares. You are allowed to drag a chip to a square 5 places from its current location, either clockwise or counterclockwise. The purpose of the puzzle is to have the chips in the originally occupied four squares but in the reverse order, or to determine that this is not possible.

You always play on the left board. The right one is very helpful and it may be worth your while to figure out its relationship to the left board.

  <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>


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