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 Liars can figure (Posted on 2017-04-24)
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.

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 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

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