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.)

 Apr 4, 2023

Let's consider the two colors Sam has as color A and color B. We can list out the possible ways he can color the equilateral triangle:

  1. All three sides have color A (AAA).
  2. All three sides have color B (BBB).
  3. Two sides have color A and one side has color B (AAB).

Note that when the triangle has two sides of color A and one side of color B, there is only one distinct coloring, as rotating or reflecting the triangle would still result in the same AAB configuration.


Therefore, Sam can color the equilateral triangle in 3 different ways.

 Apr 4, 2023

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