5. (3 points) In a room, knights who always tell the truth and liars who always lie have gathered (both are definitely present). They were asked the question: "How many liars are in the room?". To this question, all possible answers from 1 to 100 were received (some possibly multiple times). How many liars could there actually be?
Answer: 99 or 100.

## Solution:

Since a total of 100 different answers were received and one of them is definitely correct, the remaining 99 answers are incorrect. This means there are at least 99 liars in the room. There cannot be more than 100 liars, as the correct answer does not exceed 100.

Let's now confirm that both answers are possible. Indeed, there can be 99 liars when there are 100 people in the room and all give different answers, and 100 liars when there are 101 people, and some incorrect answer is given by two people.