The students of a school formed a circle. Jonas and Amanda, who were not in the circle, decided to count the students in the circle, but each starting with a different student, although following the same direction. Marcos was number 37 in Jonas's count and number 15 in Amanda's count. Nair was number 3 in Jonas's count and number 201 in Amanda's count. How many students does the school have?
Solution

Jonas and Amanda's counting was in the same direction, and they counted the same number of students in the circle. From Marcos to Nair, according to Amanda's count, there are $201-14=$ 187 students. This result should be the same in Jonas's count. Since Nair was number 3 in Jonas's count, it means that Jonas counted to the last student in the circle and then started counting again, counting 3 more. If he started from 37, then we should subtract 36 from the total number of students in the circle and then add 3, so that the result is 187, that is, the total number of students in the circle is $187+36-3=220$. We cannot forget that Jonas and Amanda are also students at the school, but they were not in the circle. Therefore, the total number of students at the school is $220+2=222$.

Note: Another way to solve the problem is to use an equation. Using $x$ for the number of students in the circle and noting that the counts of Jonas and Amanda, from Marcos to Nair, should give the same result, we have:

$$
\begin{aligned}
x-36+3 & =201-14 \\
x-33 & =187 \\
x & =187+33 \\
x & =220
\end{aligned}
$$

Thus, we conclude that the number of students at the school is $220+2=222$.