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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(2): solution | Comment 4 of 16 |

I agree with Charlie's solution just as written.  With 6 different answers, there are 5 or 6 liars.  If there were six, the answers would have been 0, 1, 2, 3, 4, 5, which is also consistent with 5 liars, so the truth cannot be deduced.  Therefore, the answers were not  0, 1, 2, 3, 4, 5.  Therefore, there were not 6 liars.  Therefore, there were 5 liars.  The answers must have been 5, 6 and four other numbers between 0 and 4.
 Posted by Steve Herman on 2015-11-15 07:39:15

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