Networks/graph theory

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

Fermat's Poser

Age

14 to 16

Challenge level

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

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

Cube Net

Age

16 to 18

Challenge level

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

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
Dice, Routes and Pathways

This article for teachers discusses examples of problems in which there is no obvious method but in which children can be encouraged to think deeply about the context and extend their ability to think mathematically, especially geometrically.