4. (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 every second person in this room is a liar."

The second one said: "Exactly every third person in this room is a liar."

and so on

The person with number $n$ said: "Exactly every ( $n_{33} 1$ )-th person in this room is a liar."

How many people could have been in the room, given that not all of them are liars?
# Answer: 2

Solution:

According to the condition, there is at least one knight among these people. Therefore, there must be at least two people, otherwise the first person would be a knight who is lying.

Moreover, there is exactly one knight, as all the speakers contradict each other. Thus, there cannot be more than half knights. On the other hand, all the islanders, including the knight who tells the truth, claim that there are at least half knights. Therefore, there must be exactly half, i.e., there are two people in the room.