All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Logic > Liars and Knights
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)

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution P's and Q's Comment 11 of 11 |

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
Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (8)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2017 by Animus Pactum Consulting. All rights reserved. Privacy Information