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I don't get this

 

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.)

 Jan 28, 2023
 #1
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There are 4 ways to do this. Here are the cases:

 

1. Only one color.

There's two ways to do this: all color one, or all color two. 

 

2. Two colors.

There's two ways to do this: One side color one and two sides color two, or two sides color one and one side color two. 

 

Every other arrangement can be rearranged to get this.

 

That's a total of 4. 

 Jan 28, 2023

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