Four inhabitants of the island make the statements as given below. Each of these inhabitants are either Liars or Knights. Little is known regarding the identity of the four inhabitants except for the fact that Q and R are not both Knights.

P's Statement: If asked, Q would say that he and S belong to the same group.

Q's Statement: If asked, S would say that he and P do not belong to the same group.

R's Statement: P and myself belong to the same group..

S's Statement: If asked, P would say that he and R do not belong to the same group.

To what group or groups do the four speakers belong?

R is either a knight or a liar. If R is a knight, then P is the same group, so P is a knight. If R is a liar, then P is a different group, so P is a knight. Either way, P is a knight. Therefore, S cannot say that he and P are different groups because that would be saying that he is a liar. Q said that, so Q is a liar. Since P is a knight, Q would say that he and S are of the same group. Q is a liar, so they are of different groups. Therefore, S is a knight. Then, P would say that he and R are of different groups, so R is a liar.

P:Knight

Q:Liar

R:Liar

S:Knight

 

Posted by Math Man on 2011-04-01 21:32:49