Pedro wants to paint a cubic box in such a way that the faces that share an edge are painted in different colors. Calculate the minimum number of colors that will be needed to paint the box in this way.
A cube has six distinct faces, two by two opposite, so that opposite faces do not share an edge. We have three pairs of opposite faces, so three colors are sufficient, as it is enough to paint the opposite faces the same color. On the other hand, it is clear that just two colors would not be enough.