The faces of a cube are painted so that any two faces which have an edge in common are painted different colors. What is the smallest number of colors required? 2 3 4 5 6

3 colors are required.

Step-by-step explanation:

3 colors are required.

We get this because the only way the same color of paint doesn't touch the same edge if it's on the opposite side. There are 3 pairs of opposite sides on our cube, so we must have 3 different colored paints.