In a remote island, all the inhabitants are either knights, who always speak truthfully or liars, who always speak falsely.
Ten natives of the island are engaged in a conversation. A visitor from a nearby island approaches the natives and, asks them: "How many of you are knights?"
Each of the ten natives answer in turn: 3, 2, 5, 7, 3, 0, 4, 4, 3, 5
In reality, how many of the ten natives are knights?
They can't be all truth telling knights because they all give different answers.
So there is at least one liar. Given this, and the fact that there are 6 different answers given, there are at least 5 liars, or at most 5 truth telling knights.
There can't be all liars, as there is the one person who did in fact say 0, and that would make him telling the truth. This gives us the fact that there is at least one truth telling knight. Given this, we know that at least one of the answers given is right, meaning that there are either 2, 3, or 5 truth telling knights. (0 and 7 have already been eliminated.)
Because the only answer given the same number of times is 3, then there are 3 truth telling knights.
Posted by Joshua
on 2012-08-27 15:10:04