Jancsi usually waits for Juliska at the metro station in the afternoon. Once, he waited for 12 minutes, during which 5 trains arrived at the station. On another occasion, he waited for 20 minutes - this time Juliska arrived with the seventh train. Yesterday, Jancsi waited for 30 minutes. How many trains could have arrived at the station in the meantime, given that the time between the arrival of two metros is always the same?
Suppose that $d$ minutes elapse between the arrival of two trains, and that the trains stay at the station for a negligible amount of time. Let's examine what bounds can be derived for $d$ based on the conditions!

On Jancsi's 12-minute wait, 5 trains arrived. In the case of the least frequent schedule, this can be imagined as Jancsi arriving at the station at the same time as a train and leaving with Juliska when the fifth subsequent train arrived; thus, he spent exactly $4d$ minutes at the station. In the case of the most frequent schedule, the 12-minute wait could have occurred if Jancsi ran in just as a train was leaving, waited for five trains, lingered a bit longer - perhaps Juliska was sick that day - and left before the sixth train arrived. Thus,

\[
\begin{aligned}
& 4d \leq 12 < 6d, \text{ from which } \\
& 2 < d \leq 3
\end{aligned}
\]

On the other occasion, however, Juliska arrived at the end of the 20th minute, so depending on whether Jancsi started waiting at the same time as he observed the arrival of a train or just as a train was leaving,

\[
6d \leq 20 \leq 7d
\]

which gives

\[
\frac{20}{7} < d \leq \frac{10}{3}
\]

Combining the obtained conditions, we get for the frequency of the trains that

\[
\frac{20}{7} < d \leq 3
\]

During the 30-minute wait, Jancsi could have observed the arrival of at least 10 and at most 11 trains. More than 11 trains would have required observing for at least $11d$ minutes, which is certainly more than $220/7$ minutes, and conversely, fewer than 10 trains could only have been observed arriving in less than $10d$ - and thus certainly less than 30 minutes.

Both scenarios are possible, for example, if $d=2.9$ minutes, which is just feasible. If Jancsi arrived 0.1 minutes after a departing train, then the tenth train arrived $2.8 + 9 \cdot 2.9$ minutes later, Jancsi waited 1.1 minutes, and then left with or without Juliska. If, however, Jancsi arrived at the station 1 minute before a train, and Juliska arrived with the 11th metro, then during his half-hour wait, Jancsi could have observed exactly eleven trains arriving.