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)?

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