Twelve balloons are arranged in a circle as shown. Counting clockwise, every third balloon is popped. $C$ is the first one popped. This continues around the circle until two unpopped balloons remain. The last two remaining balloons are
(A) $B, H$
(B) $B, G$
(C) $A, E$
(D) $E, J$
(E) $F, K$

![](https://cdn.mathpix.com/cropped/2024_04_20_6ed09463f225f8ba1f07g-153.jpg?height=442&width=426&top_left_y=316&top_left_x=1424)
Solution

The first ten balloons are popped in the following order: $C, F, I, L, D, H, A, G, B$, and $K$. The remaining two balloons are $E$ and $J$.

#