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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?

Encircling

Age 14 to 16 Challenge Level:

The shape shown is of an equilateral triangle sitting on top of a square.

What is the radius of the circle that circumscribes this shape?

Encircling

Symmetry. Creating and manipulating expressions and formulae. 2D shapes and their properties. Circle properties and circle theorems. Inequalities. Networks/Graph Theory. Regular polygons and circles. Generalising. Mathematical reasoning & proof. Quadratic equations.