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

Home > Logic > Liars and Knights
A horse of a different color (Posted on 2006-09-26) Difficulty: 2 of 5
A native, either a knight or a liar, once pointed to a man sitting below a tree and told me "If asked, that man would say I'm not the same type as he is."

What can you deduce about the native or the man?

See The Solution Submitted by e.g.    
Rating: 3.5000 (8 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution answer | Comment 19 of 22 |
It is given that the native is a knight or liar, but it is not given that the man sitting below a tree is limited to one of the categories of knight or liar.

If the native were a knight, then the tree-shaded stranger would give an answer congruent to "I'm not the same type as he (the knight) is". Thus, the tree-shaded man could not be a knight, yet this does not make the tree-shaded stranger a liar. He could be a knave, normal, or some other type.

Given the native was a liar, if the tree-shaded man were a knight the tree-shaded man would have answered the question with an answer congruent to "I'm not the same type as he (the liar) is". This answer would have the native, a liar, making a true statement -- a contradiction, thus the tree-shaded man could not be a knight.

Given the native was a liar, if the tree-shaded man were a liar the tree-shaded man would answered the question (assuming he would have answered) with an answer NOT congruent to "I'm not the same type as he (the liar) is", i.e., "I'm the same type as he (the liar) is". Such a statement could not have been made by a liar, as it would be a true statement -- a contradiction, thus the tree-shaded man could not be a liar (who provided an answer similar to that given).

In conclusion, nothing new is known of the native. He is either a knight or a liar. What is known is that the tree-shaded man is not a knight and likely not a liar, yet he could be knave, normal, or some other type.
  Posted by Dej Mar on 2011-09-11 00:02:41
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 (11)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2024 by Animus Pactum Consulting. All rights reserved. Privacy Information