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Four Triangles Puzzle

Cut four triangles from a square as shown in the picture. How many different shapes can you make by fitting the four triangles back together?

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Three Squares

What is the greatest number of squares you can make by overlapping three squares?

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A City of Towers

In this town, houses are built with one room for each person. There are some families of seven people living in the town. In how many different ways can they build their houses?

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