Wednesday, May 14, 2014

Daily 3: The Stomachion

The Stomachion is a puzzle attributed to Archimedes, and consists of 14 polygonal pieces. The object is to arrange the pieces into a square or other shape like those seen here.

After toiling for what seemed an eternity, this is the closest I got to solving Archimedes' Stomachion puzzle on Geogebra. If only I could have flipped the right triangle over rather than only rotate it, I would have finished. But, alas...

As it turns out, there are 17,152 solutions to the Stomachion, as discussed here. However, many of these are simply rotations or reflections of other solutions, with 536 unique solutions. This is surprising, given the amount of time it took me to find just one.

A primary advantage of using a physical version of the puzzle over the Geogebra version is the ability to flip pieces, which gives access to more of the 536 solutions. However, with the physical version, we are unable to easily determine the dimensions of the puzzle. We know that it is a square, but we do not know by looking at the pieces whether it should be a 10 by 10 square, 12 by 12, or so on. Knowing the dimensions of the square was one advantage of the online version of the puzzle.

I found other online versions of the puzzle like this one that did allow you to mirror the images, but it seems to have consolidated some of the pieces together. Using the puzzle above, I reproduced my solution with the pieces given and the ability to flip the pieces.

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