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An Identity Problem (Posted on 2006-08-17) Difficulty: 2 of 5
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?

See The Solution Submitted by K Sengupta    
Rating: 3.5000 (2 votes)

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Solution Minding the P's and Q's (and R's and S's)...[a solution] | Comment 2 of 11 |

From R's statement, P must be a Knight.
Then as P is a Knight it can be derived from P's statement, S must be a Knight.
Then as S is a Knight it can be deduced from S's statement, R must be a Liar.
Then from Q's statement, in order to conclude that both S and P are Knights, Q must be be a Liar.

Therefore:
P & S are Knights.  Q & R are Liars. 


  Posted by Dej Mar on 2006-08-17 14:01:32
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