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

Home > Logic > Liars and Knights
Liars can figure (Posted on 2017-04-24) Difficulty: 3 of 5
The annual round-table meeting pf the L&K Island's government meeting requires quorum of 5 members.
(i). Assuming that there are n members present and each one declares:
"I'm sitting between 2 Liars."
Can you estimate how many of them are Liars?

Another Liar arrives and takes a seat between 2 members and declares:
"I'm sitting between 2 Liars."
Apparently he is coherent (i.e. he lies) no matter where he placed himself.

(ii). Knowing that, would you change your answer to question (i)?

See The Solution Submitted by Ady TZIDON    
Rating: 2.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution Comment 4 of 4 |
There cannot be two consecutive knights, and there cannot be more than two liars in succession.  So for part(i), the maximum number of liars is (2/3)n [K-L-L], the minimum is (1/2)n [K-L].

For a quorum of 5, the order would be K-L-K-L-L.  For 6, it could be K-L-L-K-L-L, or it could be K-L-K-L-K-L.  For 7, it could be only K-L-K-L-K-L-L.

For part(ii), if a liar is added, then there cannot be two liars in a row since the addition could result in having 3 liars in succession.  Thus, there must be an even number of members, and the order must alternate between knights and liars.

Liars = n/2
Smallest n = 6

  Posted by hoodat on 2017-05-26 20:56:58
Please log in:
Remember me:
Sign up! | Forgot password

Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (10)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Copyright © 2002 - 2018 by Animus Pactum Consulting. All rights reserved. Privacy Information