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?
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