Question 72
On the island Chenonc'è there are 2009 inhabitants, divided into three clans: the scoundrels who always lie, the knights who never lie, the pages who lie one day yes and one day no, independently of one another. One day I ask each of the inhabitants how many scoundrels there are on the island. The first says: "there is at least 1 scoundrel"; the second says: "there are at least 2 scoundrels"; ... the 2009-th says: "there are at least 2009 scoundrels". I write in a list the sequence of the 2009 answers, in the order in which they were given. The next day I question all the inhabitants in the same way (not necessarily in the same order), and I obtain a list of answers identical to the one of the previous day. Knowing that there is only one knight on the island, how many pages are there?
(A) None
(B) 670
(C) 1004
(D) 1338
(E) 1339 .
(A) None
(B) 670
(C) 1004
(D) 1338
(E) 1339 .