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.
First, ignoring that you were able to deduce the number:
There could be 6 liars, claiming 0, 1, 2, 3, 4 and 5 respectively.
There could be 5 liars, claiming 0, 1, 2, 3, 4 and 5 respectively, or any other set of answers that includes a 5.
So if the answers were 0, 1, 2, 3, 4, 5, you would not have been able to deduce whether there were 5 or 6 liars.
As there had to be at least 5 liars and there can't have been 6 liars, there must have been 5 liars, assuming there was in fact a set of answers that allowed you to make this conclusion.
Various of these possibilities exist, each including one person telling the truth, 5, and one person saying 6. Or, actually other weird possibilities exist, like 2, 4, 5, 7, 100, 111, but in that case you wouldn't have been able to tell if there were 5 or 6 liars, so there really were no "off the wall" answers above 6.
Posted by Charlie
on 2015-11-13 10:50:54