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The Stomachion

From 1998 to 2008, a team of researchers worked to unravel the secrets of a document first written in Byzantine Greek over 1000 years ago (check out this TED talk by the lead researcher, William Noel). Over the centuries, monks periodically cleaned off the markings on the document, and wrote fresh text, thus creating a palimpsest. The team discovered that the palimpsest contained a copy of previously unknown work by Archimedes, the greatest of ancient mathematicians and scientists. Mathematicians pored over his work.

The Archimedes Palimpsest contained what is believed to be the first dissection puzzle. The Stomachion is a dissection of a square, resembling the tangram, but pre-dating the tangram by over 1000 years. Archimedes used 14 pieces, and some believe he was using the various arrangements that make a square to study combinatorics . Mathematicians Fan Chung and Ron Graham noted that 3 pairs of his pieces appear next to each other in all the square dissections. They suggested these be merged into a single pieces, leaving 11 pieces, which they called the Stomach. We use 11 pieces as well.

There are multiple solutions with the eleven pieces. If consider two solutions to be the same if you can get from one to the other by rotating the solution, or flipping it over, then there are 268 distinct solutions. Remarkably, starting from one solution, it is possible to step through 266 of the solutions by flipping or rotating a subset of the pieces.

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