You may also like

problem icon

Construct-o-straws

Make a cube out of straws and have a go at this practical challenge.

problem icon

Matchsticks

Reasoning about the number of matches needed to build squares that share their sides.

problem icon

Tangram Paradox

How can the same pieces of the tangram make this bowl before and after it was chipped? Use the interactivity to try and work out what is going on!

Face Painting

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

We received this solution from someone who didn't give their name:

In a tetrahedron any two faces have a common edge so no two faces can be the same colour. A tetrahedron needs 4 colours. If we start by colouring one face, then the 3 faces adjoining it need 3 more colours.

A cube needs at least 3 colours because 3 faces meet at a point. Three colours are sufficient because each pair of opposite faces can be painted in one of the 3 colours.

An octahedron needs 2 colours. At each vertex 4 faces meet and they can be painted in alternate colours.

A dodecahedron needs at least 4 colours because if we start by colouring one face then we have to use 3 more colours to paint the faces around it. The net shows how the dodecahedron can be painted with 3 faces of each colour so 4 colours are sufficient.

dodecahedron net coloured with four colours
An icosahedron needs at least 3 colours because we have to use 3 colours to paint the 5 faces around each vertex. Three colours are sufficient as shown in the net. Net of icosahedron