7. A number of students from a certain district participate in a mathematics competition, with each student's score being an integer. The total score is 8250, the top three scores are $88, 85, 80$, and the lowest score is 30 points. No more than 3 students can have the same score. How many students at least scored no less than 60 points (including the top three)?
To minimize the number of students scoring no less than 60 points, first satisfy that each score from 30 to 59 has 3 people, then the used scores are $3 \times (30+31+\cdots+59) = 4005$; then satisfy that high-scoring people are as many as possible, since $3 \times (79+78+\cdots+61) = 3990$, at this point $4005 + 3990 + 88 + 85 + 80 = 8248 < 8250$, thus there are more than $3 \times 19 + 3 = 60$ students scoring no less than 60 points. When there are 61 students scoring no less than 60 points, in addition to the aforementioned 60 students, adjust one student from 58 points to 60 points, which meets the requirement. Therefore, at least 61 students score no less than 60 points.