Puzzle Booklet - F and U Compatibility

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Time
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Category: Assembly 2D Packing
Description
One of a series of booklets produced in Hungary by hand in limited editions; their contents are made of laser cut wood.
Two shapes are called compatible if there exists a figure that can be created using either some pieces only of the first shape or some pieces only of the second shape.
Goal
The first goal is to show that F and U pentominoes are compatible?
There are other challenges:
1- Create the same shape using 2F plus 1U and 1F plus 2U.
2- Create the same shape using 3F plus 1U and 1F plus 3U.
3- Create the same shape using 7F and 7U!
4- Put back the pieces into the booklet such that there is a symmetrical arrangement of holes.
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