Question

Teresa wanted to paint each face of a cube so that the adjacent faces were different colors. She wanted to use fewer than six colors. What is the fewest number of colors she could use?

Answer 1

Teresa can paint each face of a cube with no two adjacent faces sharing the same color using only three colors by painting opposite faces the same color.

Step-by-step explanation:

The fewest number of colors Teresa could use to paint each face of a cube so that no two adjacent faces are the same color is three. To visualize this, imagine the cube and its faces. We can start by painting the top face one color.

Since the bottom face is not adjacent to the top face, it can also be painted the same color as the top face. Next, we paint one of the side faces a second color. The opposite side face can also be painted this color, as it is not adjacent to the first side face we painted.

Finally, the remaining two side faces must be painted a third color to ensure they are not adjacent to any faces of the same color. By alternating the colors for each pair of opposite faces, Teresa can ensure that no two adjacent faces share the same color while using only three distinct colors.