AMC 10B/12B 2025 (Problem 16/13)

A circle has been divided into

6

sectors of different sizes. Then

2

of the sectors are painted red,

2

painted green, and

2

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?

A circle divided into six differently sized sectors colored red, green, and blue

\text{(A)}\;12

\text{(B)}\;16

\text{(C)}\;18

\text{(D)}\;24

\text{(E)}\;28