The students are evenly spaced in a circle.
The third student is directly opposite the tenth student.
This means that the number of students between the third student and the tenth student (going in one direction) plus the number of students between the third student and the tenth student (going in the other direction) is equal to the total number of students minus 2 (excluding the third and tenth students themselves).
The number of students between the third and tenth student in one direction is $10 - 3 - 1 = 6$.
The number of students between the third and tenth student in the other direction is also 6.
The total number of students is $6 + 6 + 2 = 14$.
However, if we go around the circle in the other direction, the number of students between the third and tenth student is $n - (10 - 3) - 1 = n - 7 - 1 = n - 8$.
The number of students between the third and tenth student in one direction is $10 - 3 - 1 = 6$.
The number of students between the third and tenth student in the other direction is $n - (10 - 3) - 1 = n - 8$.
Since the third and tenth students are opposite, the number of students between them in one direction plus the number of students between them in the other direction is equal to $n - 2$.
Thus, $6 + n - 8 = n - 2$, which is $n - 2 = n - 2$. This equation is always true.
The total number of students between the third and tenth student is $6 + 6 = 12$.
The total number of students is $12 + 2 = 14$.
The distance between the third and tenth student is 7.
Since they are opposite, the distance from the third student to the tenth student is half the number of students, so $\frac{n}{2} = 7$.
Therefore, $n = 14$.
There are 14 students in the circle.
Final Answer: The final answer is $\boxed{14}$