Decision Resources

Doodles

Age 14 to 16 Challenge Level:

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

Tree Graphs

Age 16 to 18 Challenge Level:

A connected graph is a graph in which we can get from any vertex to any other by travelling along the edges. A tree is a connected graph with no closed circuits (or loops. Prove that every tree has exactly one more vertex than it has edges.

Magic Caterpillars

Age 14 to 18 Challenge Level:

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

Stringing it Out

Age 14 to 16 Challenge Level:

Explore the transformations and comment on what you find.

Tourism

Age 11 to 14 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.

Maximum Flow

Age 16 to 18 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.

Some Circuits in Graph or Network Theory

Age 14 to 18

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

Production Equation

Age 16 to 18 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?

Flow Chart

Age 11 to 14 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.

Procedure Solver

Age 16 to 18 Challenge Level:

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

Zeller's Birthday

Age 14 to 16 Challenge Level:

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

Painting by Numbers

Age 16 to 18 Challenge Level:

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

Torus Patterns

Age 16 to 18 Challenge Level:

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

Weekly Challenge 14: Mad Robot

Age 16 to 18 Short Challenge Level:

A weekly challenge: these are shorter problems aimed at Post-16 students or enthusiastic younger students.

Weekly Challenge 41: Happy birthDay

Age 16 to 18 Challenge Level:

A weekly challenge concerning the interpretation of an algorithm to determine the day on which you were born.

The Olympic Torch Tour

Age 14 to 16 Challenge Level:

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

Drug Testing

Age 16 to 18 Challenge Level:

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

Mystery Procedure

Age 14 to 16 Challenge Level:

Can you work out what this procedure is doing?

Sorted

Age 16 to 18 Challenge Level:

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

Simply Graphs

Age 16 to 18 Challenge Level:

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