Red or Black
How many edges of a cube need to be coloured black to mean every face has at least one black edge?
Age
11 to 14
Challenge level
Problem
Each edge of a cube is coloured either red or black.
If every face of the cube has at least one black edge, what is the smallest possible number of black edges?
Student Solutions
Image
Each edge of the cube borders two faces.
As there are six faces, a minimum of three black edges will be required.
The diagram on the right shows that three black edges is enough.