The project is a more involved problem than those used for the Problem of the Week. In some cases, it may be helpful to use Sketchpad or some other drawing program to help in preparing a solution.
Solutions will be accepted from teams of no more than four students. The team submitting the most complete solution will receive Geometry Forum t-shirts. Solutions must be received by Thursday, March 31 to be considered. Anything may be used to reach a conclusion, but solutions must be submitted electronically. Computer-constructed documents, such as Sketchpad sketches or graphics files, may be sent - the answer does not have to be just in text form.
Note: You don't have to _prove_ the answer to submit your solution. Just provide a convincing argument for your claim. This may include an explanation with accompanying pictures, or perhaps a well-documented Sketchpad sketch.
Submissions should include the names, grade(s), and school of the team members. Mail them to firstname.lastname@example.org. DO NOT POST YOUR ANSWER! If you have questions about how to submit any accompanying documents, just send mail. You may send NeXT mail to email@example.com. Please cc a copy to firstname.lastname@example.org so that we'll know to check mail there. Submissions are welcome from non-high school students, but you won't be eligible for the awesome t-shirts! :-)
Project of the Month for March 1994
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, there is 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.)