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

Home > Logic > Liars and Knights
Knowing the Natives (Posted on 2003-08-16) Difficulty: 2 of 5
I met two natives on an island - Benny and Lenny. They are either a knight, a liar or a knave. Knights always tell the truth, liars always lie and knaves alternate between truth and lie. They tell me this:

Benny : We are both of the same type.
Lenny : I am a knave.
Benny : Lenny is a liar.

A knight then tells me what Lenny is. From this I was able to work out what they were.

What are Benny and Lenny?

See The Solution Submitted by Lewis    
Rating: 3.8000 (5 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution Puzzle Solution | Comment 13 of 14 |
(In reply to Answer by K Sengupta)

At the outset, Lenny cannot be a knight since no knight will falsely proclaim himself as a knave.

Assume that Benny is a knight. If so, then in terms of his first statement it follows that Lenny is a knight. This is a contradction.

So, neither Benny, nor Lenny can be a knight. Now, if both Benny and Lenny are liars, then Benny's truthfully spoken 2nd statement is a contradction.

Thus, the valid choices are:

Benny      liar        knave      knave
Lenny     knave       liar         knave

Now, if the visitor was told that Lenny is a knave, it would be impossible for him to resolve Benny's type, since in terms of the above table, Benny can either be a liar or a knave. On the other hand, knowing that Lenny is liar will immediately enable the visitor to establish that Benny is a knave.

Consequently, the visitor was told that Lenny is a liar and he deduced that Benny is a knave. 

Edited on July 5, 2008, 1:02 pm
  Posted by K Sengupta on 2008-05-14 16:03:00

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