Decision Resources

Magic Caterpillars

Stage: 4 and 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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

Stringing it Out

Stage: 4 Challenge Level: Challenge Level:1

Explore the transformations and comment on what you find.

Tourism

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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

Stage: 5 Challenge Level: Challenge Level:1

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

Stage: 4 and 5

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

Production Equation

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

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

Stage: 3 Challenge Level: Challenge Level:1

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

Stage: 5 Challenge Level: Challenge Level:1

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

Zeller's Birthday

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

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

Painting by Numbers

Stage: 5 Challenge Level: Challenge Level:1

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

Torus Patterns

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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

Weekly Challenge 14: Mad Robot

Stage: 5 Short Challenge Level: Challenge Level:1

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

Weekly Challenge 41: Happy birthDay

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

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

Weekly Challenge 1: Inner Equality

Stage: 4 and 5 Short Challenge Level: Challenge Level:1

Our first weekly challenge. We kick off with a challenge concerning inequalities.

The Olympic Torch Tour

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

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

Drug Testing

Stage: 5 Challenge Level: Challenge Level:1

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

Mystery Procedure

Stage: 4 Challenge Level: Challenge Level:1

Can you work out what this procedure is doing?

Sortedlive

Stage: 5 Challenge Level: Challenge Level:1

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

Simply Graphs

Stage: 5 Challenge Level: Challenge Level:1

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