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Help does anybody know

 

Sam wants to color the three sides of an equilateral triangle.  He has two different colors to choose from.  In how many different ways can Sam color the sides of the triangle?  (Two colorings are considered the same if one coloring can be rotated and/or reflected to obtain the other coloring.)

 Feb 1, 2023
 #1
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Method 1: Brute Force

Usually not a good idea, but in this case it is simple so it will work.

Lets say one color is x and other is y.

xxy

xyx

yyx

yxy

4 ways.

Method 2: Logical thinking

So you can think. If i put xxy as a way, then any way with 2 x's touching is not going to be a solution, since you can rotate it. so the only other way with 2 x's is xyx. Then the same thing with y's giving you 4 solutions.

 Feb 1, 2023

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