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Doodles
Draw a 'doodle' - a closed intersecting curve drawn without taking pencil from paper. What can you prove about the intersections?
Russian Cubes
I want some cubes painted with three blue faces and three red faces. How many different cubes can be painted like that?
Picture Story
Can you see how this picture illustrates the formula for the sum of the first six cube numbers?
Age 14 to 16
Challenge Level
Prove that if $a^2+b^2$ is a multiple of $3$ then both $a$ and $b$ are multiples of $3$.
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NRICH is part of the family of activities in the Millennium Mathematics Project.
NRICH is part of the family of activities in the Millennium Mathematics Project.