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.

For N inhabitants, the number of claims of truth-tellers would be equal to N minus 2 times the number of groups of the adjacent minority delimited by one or more of the majority, or where there is no minority or majority, the inhabitants of like-kind delimited by their opposite-kind.

The number of truth-tellers claimed it total is equal to that that would be claimed in total by its complement.

There is only one situation where Mr. Mathwiz could get the numbers correct. That would be where there were 20 inhabitants
with 10 Knights and 10 Liars with each Knight separated from another Knight by a Liar. The reported count of truth-tellers in this singular case would be 0.

Posted by Dej Mar on 2011-06-06 01:56:28