20. Cuthbert is going to make a cube with each face divided into four squares. Each square must have one shape drawn on it; either a cross, a triangle or a circle. Squares that share an edge must have different shapes on them. One possible cube is shown in the diagram. Which of the following combinations of crosses and triangles is possible on such a cube (with the other shapes being circles)?

A 6 crosses, 8 triangles
B 7 crosses, 8 triangles
C 5 crosses, 8 triangles

D 7 crosses, 7 triangles
E none of these are possible
SolUTION
Each vertex of the cube consists of three squares each sharing a common edge with the other two. Hence each vertex must have one of each shape drawn on its three squares. Since there are 8 vertices, there must be 8 of each shape. Hence none of the options listed is possible.