You may also like


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?

Knight Defeated

Age 14 to 16 Challenge Level:

For the $2$ by $n$ board, if there is a tour then it must pass through the corner square. Is this possible?

It might help to think of the squares as vertices of a graph. Then there is an edge joining two vertices if and only if there is a knight's move between the corresponding squares.

Eight of the vertices are of degree two (only one path in and one out of that square). To construct a tour you are forced to visit these vertices in a particular order.