Liars and Knights!
An island is inhabited by both liars and knights.Every knight always tells the truth and each liar always lies. One day 12 islanders gathered together and issued a few statements.There is a mix of liars and knights amongst this group.
Two people said,"Exactly two of us are liars''.
Another four people said''Exactly four of us are liars''.
The remaining six said''Exactly six of us are liars''.
How many liars are there?
The answer is 6.
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The twelve people can be divided up into three groups: the group that says there are two liars, the group that says there are four liars, and the group that says there are six liars. We start by examining the first group. The two people in this group each say that there are two liars in all. If this were true, however, it would make anyone who says there are more than two liars a liar himself. This includes all ten members of the second and third groups. Since ten is not equal to two, the two members of the first group must be liars. Similar reasoning leads to the conclusion that the four members of the second group are liars as well. Therefore, the remaining six in the third group are the knights, who say that there are six liars. Hence, the answer is six.