At recess, students lined up in a circle to play a game. The students stood evenly spaced in the circle. The 5th person was directly across from the 14th person. How many students were in the circle?
If we imagine the students standing in a circle, the distance between the 5th person and the 14th person is 9 places. Since the students are evenly spaced, we can divide the circle into 9 segments. Each segment represents the space in between two students. Since there are 9 segments, there are also 9 pairs of students.
Therefore, there are $9+1=10$ students in the circle. Answer: $\boxed{10}$.
To find the number of students in the circle, we need to determine the total number of students between the 5th person and the 14th person.
Since they are directly across from each other in a circle, the total number of students between them is (14 - 5) - 1 = 8 - 1 = 7.
Now, since the students are evenly spaced in the circle, we know that the total number of students in the circle must be a multiple of 7.
So, we can start with 7 and keep increasing it until we find a multiple that satisfies the given conditions.
Multiples of 7 are: 7, 14, 21, 28, 35, 42, 49, ...
By checking these multiples, we find that the total number of students in the circle is 28.
Therefore, there were 28 students in the circle.