Valise Squeeze Puzzle

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Time
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Category: Assembly 2D Packing
Description
This puzzle is an exchange puzzle by Stan Isaacs for the International Puzzle Party 25 held in Helsinki, Finland 2005.

This is a "lost area" assembly puzzle; It can go together in several different ways, which seem to gain or lose area. It's a new version of an old puzzle from the end of the 19th century. It is in W.W. Rouse Ball's Mathematical Recreations and Essays, and may have been originated by Sam Loyd. It was studied by Lewis Carroll, who called it "A Geometrical Paradox".
Goal
The goal of the puzzle is to pack the pieces into the valise. Then repack the pieces, to squeeze in an extra yellow square. Then repack again, to squeeze in a second square, and a final time to squeeze in all three squares. (The key is to help you push out the squares when you are repacking the valise.) Once you have solved the puzzle, try to figure out where all the extra area is coming from
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