Three, a city has $n$ high schools, the $i$-th high school sends $C_{i}$ students $\left(1 \leqslant C_{i} \leqslant 39,1 \leqslant i \leqslant n\right)$ to the gym to watch a ball game, the total number of all students is $\sum_{i=1}^{n} C_{i}=1990$. Each row in the stand has 199 seats. It is required that students from the same school must sit in the same row. How many rows does the gym need to arrange at least to ensure that all students can be seated?
12
III. 【Analysis and Solution】The conclusion is that at least 12 rows are needed to ensure that all students can be seated. Number the schools, and let the students from the 1st school sit in the 1st row, followed by the students from the 2nd school, and so on. Each school's students sit together, and when a row is full, the remaining students from the same school can start the next row. Since each row has 199 seats and the total number of students is 1990, after 10 rows, all students will be seated. Then, adjust the students at the breaks, i.e., if the end of the 1st row and the beginning of the 2nd row are students from the same school, move all students from that school out, and so on. This way, at most 9 schools' students will be moved out. Since each school has at most 39 students, and \(5 \times 39 = 195 < 199\), the first 5 schools' students can be seated in the 11th row, and the remaining 4 schools' students in the 12th row. Thus, it is proven that arranging 12 rows can ensure all students are seated and meet the requirement: students from the same school sit in the same row.

If only 11 rows are arranged, it may indeed not be enough. For example, suppose \(n=59\), with 58 schools each sending 34 students and 1 school sending 18 students, then \(58 \times 34 + 18 = 1990\). Since \(5 \times 34 = 170 < 199 < 204 = 6 \times 34\), except for one row that can seat 6 schools' students, the other 10 rows can each seat 5 schools' students. Therefore, 11 rows can seat at most \(6 + 5 \times 10 = 56\) schools' students, leaving 2 schools' students without seats. This shows that 12 rows are still the minimum number of rows needed to ensure all students can be seated according to the rules.