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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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Three Squares

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

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A City of Towers

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Start Cube Drilling

Stage: 1 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3
When you drill your holes, can you picture which small cubes have got holes in them?
How many do you drill holes in?
Now think about your friend.
Can you picture the small cubes that he or she drills holes in?
Are any of the cubes your friend drills ones that you've already drilled?
Are some of these cubes ones that you haven't already drilled?
The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice. More information on many of our other activities can be found here.
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NRICH is part of the family of activities in the Millennium Mathematics Project.