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's Statement:

If R = knight then R & P are knights.
If R = liar then R = liar & P = knight
Therefore P must be a knight.

P = Knight

P's Statement:

Given P is telling the truth from R's Statement: -

Assuming  Q is telling the truth then
 - Q & S are knights

Assuming Q is a liar then
 - Q = liar & S = knight

Therefore S = knight

S's Statement:

Given S is telling the truth from P's Statement: -

P is a knight so R must be a liar

Therefore R = liar

So Far P & S = Knights & R = Liar

Q's Statement:

S is a knight and P is a knight so
therefore Q must be a liar

In summary :

P & S = Knights
Q & R = Liars

Posted by Dave on 2006-08-21 10:27:00