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

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?

Rearrange the Square

Age 5 to 7
Challenge Level

Simply cutting a corner off a square can lead to a puzzling activity.
1st sq
So the little triangle is removed:

This little triangle is then put back making sure that a corner of the triangle is always touching a corner of the shape that the triangle came from, and two edges line up.

We can then make new shapes:

2 examples
Which were made as follows:

So here's the challenge: Can you make all the following and tell us about how they are made from the two shapes?

18 shapes