1. All graduates of the mathematics school took the Unified State Exam (USE) in mathematics and physical education. Each student's result in mathematics turned out to be equal to the sum of the results of all other students in physical education. How many graduates are there in the school if the total number of points scored by the students in mathematics was 50 times greater than in physical education?

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# Answer: 51.

## Solution:

Let the total number of graduates be $n$. Denote the total score in mathematics by $M$. This sum is equal to the sum of the physical education scores of all students, counted $(n-1)$ times.

Thus, we have the equation: $M=50 \frac{M}{n-1}$.

From this, the answer is

Instructions for checking:

If the problem is solved with additional assumptions, for example, that everyone scored the same, then give 1 point.