1. 3-D shapes
GM3.3 Extension Plenary
What is the least number of colours needed to paint these solids, so that no two faces next to each other are the same colour?
A cube
A tetrahedron
A square based pyramid
Preamble
Allow pupils to wrestle with this problem, before suggesting/hinting that sketching the appropriate nets might be a useful strategy, coupled with a systematic approach.
It may be necessary to explain that ‘next to’ means ‘sharing a common edge’, so faces of the same colour may meet at a point, but not along an edge.
Possible content
Visualising 3-D shapes and possibly their nets.
Resources
None – the whole exercise should only involve visualisation or, at most, sketches.
Solution/Notes
Three colours Four colours Three colours