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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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My Translation | Comment 1 of 11

Slightly misleading the way this is worded..

Going on my assumptions of how the parameters were intended to be followed, I'm going to say Q and R are lumped together as LIARS seeing as they cannot be knights. S and P are together as KNIGHTS.

P's Statement: Since P is telling the truth and Q is a liar, Q would claim that he and S belonged together despite S's partnership with P.

Q's Statement: If asked, S would say that he and P DO belong to the same group since S is a truth teller. However, the sentence is negated because Q is a liar.

R's Statement: Since R is a liar, he would be inclined to say that a member not of his group (P) would be paired with him.

S's Statement: Since S is a knight and P is a knight, it is true that P would state he does not belong to R's group (LIARS)


  Posted by Stefanie on 2006-08-17 13:42:55
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