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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?

Building with Cubes

Stage: 1 Challenge Level: Challenge Level:2 Challenge Level:2
As you picture each stage in your head, you might like to draw it so that you can keep track of where the cubes are.
You could try to describe the building to someone else after each stage to see whether you can still imagine it.