Link is coloring a triforce, which consists of four equilateral triangles and is depicted below. He has three colors to use: gold, black, and green. So that it remains recognizable, he doesn't want to color any two triangles the same color if they share a side. How many different ways can he color the triforce? (Two colorings that differ by rotation are considered distinct.)
We can first choose the color for the middle triangle, which has 3 ways.
Next, we can choose the rest of the on the outside, each of which have 2 colors to choose from.
Therefore we have the equation,
\(3 \cdot 2\cdot2\cdot2 = 24\)
So there are 24 ways he can color it