# Decision Resources

### Doodles

##### Age 14 to 16Challenge Level

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

### Network Trees

##### Age 14 to 18Challenge Level

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

### Magic Caterpillars

##### Age 14 to 18Challenge 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 16Challenge Level

Explore the transformations and comment on what you find.

### Tourism

##### Age 11 to 14Challenge 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 18Challenge 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 18Challenge 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 14Challenge 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 18Challenge Level

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

### Zeller's Birthday

##### Age 14 to 16Challenge 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 18Challenge Level

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

### Torus Patterns

##### Age 16 to 18Challenge Level

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

##### Age 16 to 18 ShortChallenge Level

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

### Happy birthDay

##### Age 16 to 18Challenge Level

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

### The Olympic Torch Tour

##### Age 14 to 16Challenge 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 18Challenge 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 16Challenge Level

Can you work out what this procedure is doing?

### Sorted

##### Age 14 to 18Challenge Level

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

### Simply Graphs

##### Age 16 to 18Challenge Level

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