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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?

Three Squares

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?

Building with Cubes

Age 5 to 7
Challenge Level

Alice from the Royal School did a sketch of the images she'd pictured in her head. Here are the two she sent us:

picture of buildings

Well done, Alice. I wonder if you can say which colour cube is hidden in each case?

A group of pupils from Lillington Primary School also sent us images of what they imagined the first building to look like:

This is from Abbie:

This is from Chelsea:

Here is Kyle's picture:

And finally, from someone else, who's name I couldn't make out, unfortunately: