Networks/graph theory

problem

Instant Insanity

Age

11 to 18

Challenge level

Given the nets of 4 cubes with the faces coloured in 4 colours, build a tower so that on each vertical wall no colour is repeated.
problem

Olympic Magic

Age

14 to 16

Challenge level

in how many ways can you place the numbers 1, 2, 3 … 9 in the nine regions of the Olympic Emblem (5 overlapping circles) so that the amount in each ring is the same?
problem

Magic W

Age

14 to 16

Challenge level

Find all the ways of placing the numbers 1 to 9 on a W shape, with 3 numbers on each leg, so that each set of 3 numbers has the same total.
problem

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?
problem

Network Trees

Age

14 to 18

Challenge level

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

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

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

Torus Patterns

Age

16 to 18

Challenge level

How many different colours would be needed to colour these different patterns on a torus?
article
Geometry and Gravity 2

This is the second of two articles and discusses problems relating to the curvature of space, shortest distances on surfaces, triangulations of surfaces and representation by graphs.
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.