Let the number of students be $n$. The last student to climb the lighthouse has got all the numbers 1 through $n$ with the lottery. As number $n$ is only available in the first round, that student had to get $n$ in the first round. As number $n-1$ is only available in 1st and 2nd round and in the 1st round that student did not get it, the student got $n-1$ in the 2nd round. Analogously, since $n-2$ is only available in the first three rounds and that student did not get it in the first two rounds, the student got $n-2$ in the 3rd round. Continuing the same way shows that the last one to climb the lighthouse got numbers $n$ through 1 in decreasing order, or got the largest available number in every round.

The rest of the students who only participated in rounds 1 through $n-1$ have to share in the first round numbers 1 through $n-1$, in the second one 1 through $n-2$, in third one 1 through $n-3$ and so on. Therefore for them this process is as if the person last to climb the tower did not participate at all and $n$ would be smaller by 1. For this holds for any $n$, all students get the numbers in decreasing order with every next one being smaller by 1, that includes Miku. This allows us to find that in the 9th round Miku got number 6.