11. (10 points) There are 20 piles of stones, each containing 2006 stones. The rule is: taking one stone from each of any 19 piles and placing them into another pile is considered one operation. After fewer than 20 such operations, one pile has 1990 stones, and another pile has between 2080 and 2100 stones. How many stones are in this pile?
【Analysis】For a pile of stones, if it is taken once, the quantity decreases by 1; if it is added once, the quantity increases by 19. Consider a pile with 1990 stones. If it is added at least once, then it can be taken at most 19 times, and the final number of stones will definitely be no less than 2006. Therefore, this pile of stones has never been added, and a total of 16 operations have been performed. Since the number of stones in another pile is between 2080 and 2100, it has only been added 5 times and taken 11 times, so the number of stones in this pile is $19 \times 5 - 11 + 2006 = 2090$.

【Solution】According to the problem, we can conclude that for a pile of stones, if it is taken once, the quantity decreases by 1; if it is added once, the quantity increases by 19.

Consider a pile with 1990 stones. If it is added at least once, then it can be taken at most 19 times, and the final number of stones will definitely be no less than 2006.

Therefore, this pile of stones has never been added, and a total of 16 operations have been performed.
Since the number of stones in another pile is between 2080 and 2100, it has only been added 5 times and taken 11 times, so the number of stones in this pile is $19 \times 5 - 11 + 2006 = 2090$.

Answer: This pile of stones has 2090 stones.