6. On the island that doesn't exist, there are 2008 inhabitants, divided into three clans: the scoundrels who always lie, the knights who never lie, and the pages who lie one day and tell the truth the next. Lorenza, visiting for two days, meets them all on the first day. The first one says: "there is exactly one scoundrel on the island"; the second one says: "there are exactly two scoundrels on the island"... the 2008th one says: "there are exactly 2008 scoundrels on the island". The next day, Lorenza questions them all again in the same order. The first one says: "there is exactly one knight on the island"; the second one says: "there are exactly two knights on the island"... the last one says: "there are exactly 2008 knights on the island".

How many pages are there on the island?
(A) 0
(B) 1
(C) 1004
(D) 2006
(E) it is not possible to determine with the data given in the problem.
6. The answer is (B). Lorenza notes that both the first and second days, all 2008 inhabitants make contradictory statements, indicating that at least 2007 of them are lying. That is, at most one tells the truth on the first day, and at most one on the second. From this, it is deduced that at least 2006 have lied both days, meaning there are at least 2006 knaves, and at most one knight in total. In reality, exactly one person told the truth on the first day, because if everyone had lied, there would be no knaves on the island, contrary to what has already been deduced. On the second day, however, no one could have told the truth, as there are no knights. If there were, the only knight would be the first inhabitant, who on the second day stated that there is exactly one knight. But this was contradicted by the first day when he stated that there is only one knave, when there are at least 2006. Now we have 2007 liars on the first day and 2008 on the second, so we deduce that 2007 are knaves and the one who told the truth on the first day is a page. (In particular, it is exactly the penultimate inhabitant who was interviewed).