Question: Each of the 6 petal flower is to be painted one of two colors. In how many different ways can this be don't? (Two flowers are the same only if one can be obtained from another by rotating the flower.)Solution below.
Solution : See below for the two images. For all of the same color, one and 5 of the same color or 2 and 4 of the same color, each has two ways when you switch to another color so 5 x 2 = 10 ways so far.
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For the 3 red and 3 yellow petals. See below for all the possibilities. The two on the left are very tricky.
They are not the same. The answer is 14 ways.
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Solution : See below for the two images. For all of the same color, one and 5 of the same color or 2 and 4 of the same color, each has two ways when you switch to another color so 5 x 2 = 10 ways so far.
For the 3 red and 3 yellow petals. See below for all the possibilities. The two on the left are very tricky.
They are not the same. The answer is 14 ways.
