Each face of a cube is painted with exactly one colour. What is the smallest number
of colours needed to paint a cube so that no two faces that share an edge are the
same colour?  Select the correct option:
A) 2 colours B) 3 colours C) 4 colours D) 5 colours E) 6 colours
Assume the top face of the cube is coloured green.   Since the front face of the cube shares an edge with the top face, it cannot be coloured green.   Thus, we need at least two colours.   Thus, we assume that the front face is coloured blue, as shown in Figure 1.   Since the right face shares an edge with the top face and with the front face, it cannot be   coloured green or blue. Thus, we need at least three colours.   Thus, we assume that the right face is coloured red, as shown in Figure 2.   We have shown that at least 3 colours are needed. In fact, the cube can be coloured with   exactly 3 colours by colouring the left face red, the back face blue, and the bottom face green   (Figure 3).   In this way, the cube is coloured with exactly 3 colours and no two faces that share an edge   are the same colour.   Therefore, 3 is the smallest number of colours needed to paint a cube so that no two faces that   share an edge are the same colour.which is=3   correct answer 3 colours
<result>B</result>
Each face of a cube is painted with exactly one colour. What is the smallest number
of colours needed to paint a cube so that no two faces that share an edge are the
same colour?