I need help on this quick


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 18, 2023

Let the colors be red and blue.


To solve, split it into cases: 


Case I (All 3 are of one color): There are 2 cases - all 3 are either red or blue


Case II (2 are one color, 1 is the other): There are 2 cases - 2 are red, 1 is blue or 2 are blue, 1 is red (Note that all the cases can be rotated or reflected to be the same thing)


So, there are \(2 + 2 = \color{brown}\boxed{4}\) cases.

 Jan 18, 2023

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