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(Repeated April 1996)

For which N's is it possible to make a perfect square using all the pieces from N sets of Tangrams?

Example: We know you can make a square with one set of tangrams. If you take all the pieces from two sets, can you make a square? How about with three sets? Four? More? Explain why some of the numbers work and some don't.

Tangrams are seven polygons that fit together to form many different shapes, one of which is a square. If you don't have access to tangrams, you can expand the picture and print it out. (There is also available on our ftp site a postscript document that is a picture of the seven pieces. You can print out as many copies of this as you would like to play around with. It will be in the /project.of.the.month directory, and will be called tangram.ps. Let me know if you have any problems with the file.)

Thanks to C. Kenneth Fan (ckfan@math.harvard.edu) for submitting this problem and helping evaluate the answers!


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2 July 1995