2018 UNM-PNM Statewide High School Mathematics Contest II Problems/Problem 8

Problem

Using red, blue and yellow colored toothpicks and marshmallows, how many ways are there to construct distinctly colored regular hexagons? (Note that two colored hexagons are the same if we can either rotate one of the hexagons and obtain the other or flip one of the hexagons about some line and obtain the other.)

Solution

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