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 6 or less liars (Posted on 2015-11-13)
In a small village there are two kinds of people: liars and truthtellers.
Everybody knows everybody and everybody knows as well who is a liar and who’s a truth-teller.
I approach six villagers and pose the same question to each of them:
"How many liars are among you?"

I get six distinct answers (integers, of course) and deduce the true one.

How many liars are in that group?

Liars always lie and truthtellers never do.

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 re: solution | Comment 3 of 16 |
(In reply to solution by Charlie)

As each of the six villagers gave a different integer, it can be immediately deduced that there are five or six liars. If any of the integers given is 5, one can not deduce whether that villager who gave that answer is a truthteller or liar - unless one of the liars answered 6. Given the truth is deduced to the number of liars that comprise the group asked, (1) there was no villager who answered 5 and all six villagers are liars - or (2), both integers, 5 and 6, were given and five of the villagers are liars (with the truthteller providing the answer 5).

Given that the true one was deduced (as opposed to the truth being deduced), it is implied that there is indeed a truthteller, thus the truthteller provided the correct answer, and there are five village liars in the group.

Edited on November 15, 2015, 5:53 am
 Posted by Dej Mar on 2015-11-15 05:04:21

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