Visualising and representing

problem
Right or left?

Age

7 to 11

Challenge level

Which of these dice are right-handed and which are left-handed?
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
Tetrahedra tester

Age

14 to 16

Challenge level

An irregular tetrahedron is composed of four different triangles. Can such a tetrahedron be constructed where the side lengths are 4, 5, 6, 7, 8 and 9 units of length?
problem
Painted cube

Age

14 to 16

Challenge level

Imagine a large cube made from small red cubes being dropped into a pot of yellow paint. How many of the small cubes will have yellow paint on their faces?
problem
Paw prints

Age

7 to 11

Challenge level

A dog is looking for a good place to bury his bone. Can you work out where he started and ended in each case? What possible routes could he have taken?
problem
A chain of eight polyhedra

Age

7 to 11

Challenge level

Can you arrange the shapes in a chain so that each one shares a face (or faces) that are the same shape as the one that follows it?
problem
Buses

Age

11 to 14

Challenge level

A bus route has a total duration of 40 minutes. Every 10 minutes, two buses set out, one from each end. How many buses will one bus meet on its way from one end to the other end?
problem
Coordinate patterns

Age

11 to 14

Challenge level

Charlie and Alison have been drawing patterns on coordinate grids. Can you picture where the patterns lead?