That was too easy...
12 people say the following statements one after another: 1: There are no honest people in this room; 2: There is at most one honest person in this room; 3: There are at most two honest people in this room . . . . . . . . . . 12: There are no more than 11 honest people in this room. How many honest people are in the room?
Man 1 has to be dishonest because, if there were no honest people, he'd be telling the truth, and would therefore be honest, creating a paradox.
Man 2 is dishonest because if he is telling the truth, only one person is honest. But if only one person is honest, then the next ten men in the room would also be telling the truth (because fewer men are honest than the maximum they said there would be), so there'd be eleven honest people, making man 2 a liar, and creating a paradox.
This continues on. If man 6 was honest, at most there'd be five honest men. Making the next six men honest, meaning there'd be seven honest men, making man 6 a liar, creating a paradox.
But, if man 7 is honest, there's at least six honest men. This makes the next five men honest, meaning there'd be six honest men. There's no paradox.
Man 8 is dishonest because there would be at most seven honest men. This is true for the next four men in the room, making five honest men. But this also makes man 6 honest because he said there were at most five honest men. So now there's six honest men, making man 6 a liar, creating a paradox.
This continues on. If man 12 was honest, at most there'd be eleven honest men, which is true since he'd be the only honest one. But if there's one honest man, this makes man 2 honest because he said there'd be 1 honest man. So now there's two honest men, making man 1 a liar, creating a paradox.
So, there can only be six honest men.