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

Home > Logic > Liars and Knights
A grok is a grok is a ... ? (Posted on 2007-06-29) Difficulty: 3 of 5
One day you meet three persons, each either a Knight or a Liar. You ask "How many of you are knights?", and the first person answers "Grok!".

Not understanding, you ask the second one "What does 'Grok' mean?", and he answers "One", but then the third one cries out "That's false!".

What can you tell about each person, if anything?

No Solution Yet Submitted by Federico Kereki    
Rating: 3.0000 (4 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution Solutions | Comment 10 of 11 |

There are 2 possible combinations.

We know right off that 2 and 3 cannot be the same because of the statement from 3.  If 3 is a Liar, then statement 2 is true meaning 2 is a Knight.  But if 3 is a Knight, then his statement is true, making 2 a Liar.  This eliminates half of the possible combinations.  The four that remain are {KKL, KLK, LKL, & LLK}.

Consider now if the second person is a knight.  This means that indeed 'Grok' = 'One'.  However, if the first person is also a Knight, his answer of 'One' would be false.  Yet if the first person is a liar, then his answer of 'One' would be true.  Thus, two more combinations are eliminated.  The two that now remain are {KLK, & LLK}.

Of the two remaining choices, both are valid if 'Grok' = 'Two'.  For anything else, only the latter remains valid.

Knight, Liar, Knight

or

Liar, Liar, Knight 


  Posted by hoodat on 2007-07-02 09:45:53
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 (3)
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