Challenge Level

Draw a 'doodle' - a closed intersecting curve drawn without taking pencil from paper. What can you prove about the intersections?

Challenge Level

Explore some of the different types of network, and prove a result about network trees.

Challenge Level

Label the joints and legs of these graph theory caterpillars so that the vertex sums are all equal.

Challenge Level

Explore the transformations and comment on what you find.

Challenge Level

If you can copy a network without lifting your pen off the paper and without drawing any line twice, then it is traversable. Decide which of these diagrams are traversable.

Challenge Level

Given the graph of a supply network and the maximum capacity for flow in each section find the maximum flow across the network.

Eulerian and Hamiltonian circuits are defined with some simple examples and a couple of puzzles to illustrate Hamiltonian circuits.

Challenge Level

Each week a company produces X units and sells p per cent of its stock. How should the company plan its warehouse space?

Challenge Level

The flow chart requires two numbers, M and N. Select several values for M and try to establish what the flow chart does.

Challenge Level

Can you think like a computer and work out what this flow diagram does?

Challenge Level

What day of the week were you born on? Do you know? Here's a way to find out.

Challenge Level

How many different colours of paint would be needed to paint these pictures by numbers?

Challenge Level

How many different colours would be needed to colour these different patterns on a torus?

Challenge Level

Can you work out what happens when this mad robot sets off?

Challenge Level

Can you interpret this algorithm to determine the day on which you were born?

Challenge Level

Imagine you had to plan the tour for the Olympic Torch. Is there an efficient way of choosing the shortest possible route?

Challenge Level

How do different drug-testing regimes affect the risks and payoffs for an athlete who chooses to take drugs?

Challenge Level

How can you quickly sort a suit of cards in order from Ace to King?

Challenge Level

Look for the common features in these graphs. Which graphs belong together?