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Square Areas

Can you work out the area of the inner square and give an explanation of how you did it?

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Kissing Triangles

Determine the total shaded area of the 'kissing triangles'.

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Hallway Borders

What are the possible dimensions of a rectangular hallway if the number of tiles around the perimeter is exactly half the total number of tiles?

Giant Rubik's Cube

Age 11 to 14 Short Challenge Level:

A Rubik’s cube is made of 3 by 3 by 3 smaller cubes – so 27 in total – but only 26 of them are visible.

How many cubes would be visible in a 12 by 12 by 12 Rubik’s cube?

This problem is adapted from the World Mathematics Championships
You can find more short problems, arranged by curriculum topic, in our short problems collection.