2. In a bag, there are marbles of various colors. It is known that all the marbles except 6 are yellow, all the marbles except 7 are red, and all the marbles except 10 are blue. Additionally, there is at least one blue marble, and there might be marbles of colors other than yellow, red, and blue. How many marbles are in the bag?
(A) It is not possible to determine
(B) 11
(C) 12
(D) 20
(E) 23
2. The answer is (B). Let's call $n$ the total number of marbles in the bag. The yellow marbles are then $n-6$, the red marbles are $n-7$, and the blue marbles are $n-10$. Since there might also be marbles of other colors, the following inequality holds: $n-6+n-7+n-10 \leq n$, which implies $n \leq \frac{23}{2}$. Since there is at least one blue marble, $n \geq 11$, hence $n=11$.