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?

Zig Zag

Age 14 to 16 Challenge Level:

Four identical right angled triangles are drawn on the sides of a square. Two face out, two face in. Why do the four vertices marked with dots lie on one line?

Quadratic equations. Making and proving conjectures. Inequalities. Number theory. Creating and manipulating expressions and formulae. Squares. Mathematical reasoning & proof. Networks/Graph Theory. Generalising. Pythagoras' theorem.

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Doodles

Russian Cubes

Picture Story

Zig Zag

Age 14 to 16 Challenge Level: