11. From the three-digit numbers $100, 101, 102, \ldots, 699, 700$, if $n$ different numbers are taken, such that there are always three numbers among them with the same sum of digits. Then the minimum value of $n$ is $\qquad$
【Analysis】Among the numbers from 100 to 700, the number with the smallest digit sum is 100, whose digit sum is 1, and there is only 1 number with a digit sum of 1; the number with the largest digit sum is 699, whose digit sum is 24, and there is only 1 number with a digit sum of 24.
The remaining numbers have a digit sum that is one of the 22 possible digit sums from 2 to 23, and each of the digit sums from 2 to 23 has at least 2 numbers.
Therefore, the minimum value of $n$ is $1+1+2 \times 22+1=47$.