12. On the Island of Knights and Rascals, knights always tell the truth and rascals always lie. During a meeting, the attendees sit around a large table and each one says: "the person to my right is a rascal." Knowing that there are fewer than 100 knights among the attendees, which of the following could be the number of participants at the meeting?
(A) 208
(B) 85
(C) 153
(D) 168
(E) 205
Problem 12. The answer is (D).

Two people sitting next to each other cannot both be liars or both be knights. Indeed, if the person on the left, of the two, is a knight, then he tells the truth, and therefore his right neighbor is a liar; conversely, if the person on the left is a liar, then he lies, and therefore his right neighbor is a knight. This shows that knights and liars alternate around the table, and therefore are in the same number; in conclusion, the number of people at the meeting is even. Knowing that fewer than 100 are knights, the total number of people is less than 200; the correct answer is found by observing that 168 is the only even number less than 200 among those listed.

(Problem proposed by F. Florian)