I am a member of a club in which every member either always lies or always tells the truth. Yesterday I had a telephone call from a member who always tells the truth and he said ‘Some members have just had dinner around a circular table, and each member said ‘I declare that the man on my left is a liar’”. Ten minutes later I received another telephone call from another member called John, and he said “I was at the dinner and there were 11 of us there”. Ten minutes after that I received yet another telephone call from a member called Tim, and he said “I was at the dinner and there were 8 of us there”. Either John or Tim was lying. But who was the liar?
If you have not tried to solve it, have a go now. For everyone else, the answer is after the break.
Well, the first assumption has to be that I am telling the truth. If that is not the case, then all bets are off and there is no answer. However, assuming this is the case, there must have been
(1) a mixture of liars and truth tellers around the table and
(2) an even number of people around the table.
(3) they alternate liar – truth teller around the table
Otherwise, everyone would not be able to say the sentence ‘I declare that the man on my left is a liar’.
So, John must be the liar. Did you solve it? Any other solutions?
I have produced an ebook containing 101 of the previous Friday Puzzles! It is called PUZZLED and is available for the Kindle (UK here and USA here) and on the iBookstore (UK here in the USA here). You can try 101 of the puzzles for free here.