Ten men sit side by side at a long table, all facing the same direction. Each of them is either a knight (and always tells the truth) or a knave (and always lies). Each of the people announces: "There are more knaves on my left than knights on my right." How many knaves are in the line?
Number the people from 1 to 10, from left to right according to their own perspective.

Person 1 is certainly lying, since he has no one to his left, and hence is a knave.

Person 10 is therefore a knight, since he has no one to his right and at least one knave (person 1) to his left.

Person 2 has exactly one knave to his left and at least one knight to his right, so he is a knave.

Person 9 has exactly one knight to his right and at least two knaves to his left, so he is a knight.

Continuing in this way, we find that person 3 is a knave, 8 is a knight, 4 is a knave, 7 is a knight, 5 is a knave, and 6 is a knight. Thus there are five knaves in the line.