# Who is the truth teller?

+1 vote
Three friends, Augustus, Brutus, and Caesar, play a game in which each decides to be either a liar or a truthteller. A liar must always lie and a truthteller must always tell the truth.

When you met these friends, you asked Augustus which he had chosen to be. You didn’t hear his answer but Brutus volunteered, “Augustus said that he is a liar.” Caesar added, “If one of us is a liar, then we are all liars.” Can you determine, for each person, whether he is a liar or a truthteller?
asked Oct 13, 2013 in Math

## 1 Answer

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Brutus has to be a liar, because in this game, it's impossible for anyone to say that he or she is a liar. Caesar is a liar, because if he was telling the truth, it would mean that he himself would be a liar, so therefore, he is not a truth teller, and he must be a liar. So since Caesars' statement was a lie, the opposite of what he said must be true. The opposite of what Caesar said would be; if one of us is a liar, then not all of us are liars. What that really means is that there is at least one truth teller among them. So that must mean that Augustus is a truth teller. To sum it up: Brutus- liar, Caesar- liar, Augustus- truth teller.

answered Oct 27, 2013 by Evoker (520 points)
selected Jul 9, 2014
really??? how did you figure this out?
I FOUND THE ANSWER MR JOHNSON :D
cool - somehow i knew you would ;)