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.) 

 Jul 6, 2021

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

 Jul 6, 2021

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