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The Origami Checkerboard Puzzle

Checkered Patterns

by Serhiy Grabarchuk


An Origami square.


How to get a 2x2 checkered pattern.


Three 2x2 checkered patterns.


Fifty 3x3 checkered patterns.
The object is simple: Take a square sheet of paper (colored at one side, and white on the other), and performing just "book folds" get a checkered pattern in the minimal number of single folds. No matter what pattern will be at the back of every final packet.

A small sample at left shows how to get a 2x2 square pattern with one colored cell.

In fact, you have three patterns 2x2, and fifty patterns 3x3 to play with; they are shown in the diagrams in this page. Numbers next to them indicate the minimal folds necessary to perform them.

The patterns were devised, solved, improved, and popularized by the following puzzle folks: Nob Yoshigahara, Koji Kitajima, Hiroshi Yamamoto, Setsuo Sasaki, Andy Liu, Tom Hull, Keiichiro Ishino, and the author.

Write us if you can improve any of these results.

Much more difficult challenges can be finding all the 4x4 checkered patterns and, then, finding their minimal solutions. Recently, Keiichiro Ishino calculated that there are 5,038 substantially different 4x4 checkered squares. Part of them have their solutions quite similar to the respective 3x3 checkered squares described here, but it is obvious that most of them are rather difficult to be optimized.
Last Updated: October 14, 2008
Posted: September 4, 2005
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