Decision Resources

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Some Circuits in Graph or Network Theory

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

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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?

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Network Trees

Age

14 to 18

Challenge level

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

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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.

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Stringing It Out

Age

14 to 16

Challenge level

Explore the transformations and comment on what you find.

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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.

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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?

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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.

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Torus Patterns

Age

16 to 18

Challenge level

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

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Mad Robot

Age

16 to 18

Challenge level

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

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Mystery Procedure

Age

14 to 16

Challenge level

Can you work out what this procedure is doing?

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Sorted

Age

14 to 18

Challenge level

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

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Simply Graphs

Age

16 to 18

Challenge level

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

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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.

Paintbrush and different coloured watercolour paint blocks.

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Painting by Numbers

Age

16 to 18

Challenge level

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

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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?

$Happy \birthDay$

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Happy BirthDay

Age

16 to 18

Challenge level

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

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Favourite

Tourism

Age

11 to 16

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.

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Procedure Solver

Age

16 to 18

Challenge level

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

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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?

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For younger learners

Decision Resources

Some Circuits in Graph or Network Theory

Doodles

Network Trees

Magic Caterpillars

Stringing It Out

Maximum Flow

Production Equation

Zeller's Birthday

Torus Patterns

Mad Robot

Mystery Procedure

Sorted

Simply Graphs

Flow Chart

Painting by Numbers

The Olympic Torch Tour

Happy BirthDay

Tourism

Procedure Solver

Drug Testing