When Mr. Mathwiz visited the IoK&L* he was surrounded by 20 or 21 male inhabitants, who formed a perfect circle and then each said a single word (either "Knight" or "Liar") about the man on his right.
The wiz then evaluated correctly the exact numbers of liars and the truth-tellers.

What were those numbers?


*IoK&L, is an imaginary island, inhabitated by Liars and by Truth-Tellers a.k.a. Knights.

(In reply to what if...? :-) by chaotic)

In the situation where there are 21 individuals and only one reported Knight, there are alternating Knights and Liars in the chain but for one link.  The link would either be two knights {K L K L K L K L K L K L K L K L K L <K K> L} or two liars {K L K L K L K L K L K L K L K L K <L L> K L}. In each of these cases the inhabitants would report the same, and thus Mr. Mathwiz would be unable to determine if there were 10 Liars and 11 Knights or 11 Liars and 10 Knights.

As a liar would not claim the person on his right to be a Knight if that person were a Knight and a Knight would not claim the person on his right to be a Knight unless the person were a Knight, there can be no report of only one Liar.

 

Edited on June 21, 2011, 12:40 pm

Posted by Dej Mar on 2011-06-21 04:13:29