10. Some edges of a cube are to be coloured red so that every face of the cube has at least one red edge. What is the smallest possible number of edges that could be coloured red?
A 2
B 3
C 4
D 5
E 6
Solution
B

A cube has six faces. An individual edge forms the boundary of only two faces. Therefore at least $6 \div 2=3$ edges must be coloured red. It is possible, as shown, to choose three edges which between them include an edge of each face. Hence the smallest number of edges that could be coloured red is 3 .