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

It can then be said that among the three:

(A) there is exactly one page

(B) there are exactly two pages

(C) there are exactly three pages

(D) there is no page

(E) the number of pages is uncertain.
22) The answer is $(\mathrm{C})$.

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.