Networks/graph theory

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
The bridges of Konigsberg

Age

11 to 18

Challenge level

Investigate how networks can be used to solve a problem for the 18th Century inhabitants of Konigsberg.
problem
Tourism

Age

11 to 14

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.
problem
Travelling salesman

Age

11 to 14

Challenge level

A Hamiltonian circuit is a continuous path in a graph that passes through each of the vertices exactly once and returns to the start. How many Hamiltonian circuits can you find in these graphs?
problem
Hamilton's puzzle

Age

7 to 11

Challenge level

I start my journey in Rio de Janeiro and visit all the cities as Hamilton described, passing through Canberra before Madrid, and then returning to Rio. What route could I have taken?
problem
Königsberg

Age

11 to 14

Challenge level

Can you cross each of the seven bridges that join the north and south of the river to the two islands, once and once only, without retracing your steps?
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
Classifying solids using angle deficiency

Age

11 to 16

Challenge level

Toni Beardon has chosen this article introducing a rich area for practical exploration and discovery in 3D geometry
problem
Networks and nodes

Age

7 to 11

Challenge level

Without taking your pencil off the paper or going over a line or passing through one of the points twice, can you follow each of the networks?
problem
Only connect

Age

11 to 14

Challenge level

The graph represents a salesman’s area of activity with the shops that the salesman must visit each day. What route around the shops has the minimum total distance?