Networks/graph theory

problem

The Olympic Torch Tour

Age

14 to 16

Challenge level

2 out of 3

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

Fermat's Poser

Age

14 to 16

Challenge level

3 out of 3

Find the point whose sum of distances from the vertices (corners) of a given triangle is a minimum.
problem

Network Trees

Age

14 to 18

Challenge level

1 out of 3

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

Magic W Wrap Up

Age

16 to 18

Challenge level

1 out of 3

Prove that you cannot form a Magic W with a total of 12 or less or with a with a total of 18 or more.
problem

Simply Graphs

Age

16 to 18

Challenge level

1 out of 3

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

Factors and Multiples Graphs

Age

16 to 18

Challenge level

1 out of 3

Explore creating 'factors and multiples' graphs such that no lines joining the numbers cross
problem

Cube Net

Age

16 to 18

Challenge level

2 out of 3

How many tours visit each vertex of a cube once and only once? How many return to the starting point?
problem

Torus Patterns

Age

16 to 18

Challenge level

3 out of 3

How many different colours would be needed to colour these different patterns on a torus?
article
Ding Dong Bell

The reader is invited to investigate changes (or permutations) in the ringing of church bells, illustrated by braid diagrams showing the order in which the bells are rung.
article
Euler's Formula

Some simple ideas about graph theory with a discussion of a proof of Euler's formula relating the numbers of vertces, edges and faces of a graph.