17) On an island, there live three categories of people: the knights, who always tell the truth, the knaves, who always lie, and the pages, who after telling a truth always tell a lie and vice versa. On the island, I meet an old man, a boy, and a girl. The old man states: "I am a page"; "The boy is a knight."

The boy says: "I am a knight"; "The girl is a page."

The girl finally states: "I am a knave"; "The old man is a page."

It can then be said that among the three:

\(\begin{array}{ll}\text { (A) there is exactly one page } & \text { (B) there are exactly two pages }\end{array}\)

(C) there are exactly three pages (D) there is no page

(E) the number of pages is uncertain.
17) The answer is (C).

The girl is indeed certainly a page: she cannot be a knight (otherwise her first statement would be true) and neither can she be a knave (otherwise her first statement would be false). Therefore, the girl's first statement is false and her second statement must be true, that is, the old man is a page. The old man's first statement is therefore true and the second must be false; so the boy is not a knight. He cannot be a knave either, otherwise his second statement would also be false, but it has been established that this statement is true. Therefore, the boy is also a page.