2. (3 points) On the Island of Misfortune, there live knights who always tell the truth, and liars who always lie. One day, $n$ islanders gathered in a room.

The first one said: "Exactly 1 percent of those present in this room are knights."

The second one said: "Exactly 2 percent of those present in this room are knights."

and so on

The person with number $n$ said: "Exactly $n$ percent of those present in this room are knights."

How many people could have been in the room, given that it is known for sure that at least one of them is a knight?
Answer: $10,20,25,50$ or 100.

Solution:

There must be exactly one knight, as all other islanders in the room contradict each other. This means that the knights are $\frac{1}{n}$ of the total number of people. Let them be $k$ percent of the total number of people present, which means the person with number $k$ told the truth.

We get $\frac{1}{n}=\frac{k}{100}$, where $k \leqslant n$.

This can be rewritten as $n k=100, n \geqslant \frac{100}{n}$. Therefore, $n$ can be any divisor of one hundred, not less than 10.