# Decision Resources

### Doodles

##### Stage: 4 Challenge Level:

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

### Tree Graphs

##### Stage: 5 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

##### Stage: 4 and 5 Challenge Level:

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:

Explore the transformations and comment on what you find.

### Tourism

##### Stage: 3 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

##### Stage: 5 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

##### 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:

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:

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:

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

### Zeller's Birthday

##### Stage: 4 Challenge Level:

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:

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

### Torus Patterns

##### Stage: 5 Challenge Level:

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:

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:

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

### The Olympic Torch Tour

##### Stage: 4 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

##### Stage: 5 Challenge Level:

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:

Can you work out what this procedure is doing?

### Sorted

##### Stage: 5 Challenge Level:

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

### Simply Graphs

##### Stage: 5 Challenge Level:

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