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Problem 16 Easy

A circle has been divided into sectors of different sizes. Then of the sectors are painted red, painted green, and painted blue so that no two neighboring sectors are painted the same color. One such coloring is shown below.

How many different colorings are possible?

Answer:D

Solution

3 ways to color region 1. When it is red, the other red can only be region 3, 4 or 5.

Case 1: Region 3 is red, then regions 4 and 6 have the same color, regions 2 and 5 have the same. 2 ways of coloring.

Case 2: Region 4 is red, then 2 ways to color regions 2 and 3 with different colors, and likewise for regions 5 and 6. There should be ways.

Case 3: Region 5 is red, same as Case 1 with 2 ways.

Thus, the total ways .