In the room, there are 12 people; some of them are honest, meaning they always tell the truth, while the rest always lie. "There is not a single honest person here," said the first. "There is no more than one honest person here," said the second. The third said that there are no more than two honest people, the fourth said no more than three, and so on until the twelfth, who said that there are no more than eleven honest people. How many honest people are actually in the room?
Note that if someone among those present lied, then all the previous ones lied as well. Such people are in the room; otherwise, the first one told the truth, and according to his words, there are no honest people in the room. For the same reason, there must be honest people in the room.

Let there be $x$ liars in the room. The last liar said that there are no more than ($x-1$) honest people in the room. Therefore, there are actually no fewer than $x$ honest people in the room. Next, the $(x+1)$-th person already told the truth about there being no more than $x$ honest people. Therefore, the number of honest people is exactly $x$, which is the same as the number of liars. Consequently, there are 6 honest people in the room.

## Answer

6 people.