The Luncheon Club
Every member of the Luncheon Club is either a truther, who always tells the truth when asked a question, or a liar, who always answers with a lie. When I visited the club for the first time, I found its members, all men, seated around a large circular table, having lunch. There was no way to distinguish truthers from liars by their appearance and so I asked each man in turn which he was. This proved unenlightening. Each man naturally assured me he was a truther. I tried again, this time asking each man whether his neighbor on the left was a truther or a liar. To my surprise each told me the man on the left was a liar. Later in the day, back home and tying up my notes on the luncheon, I discovered I had forgotten to record the number of men at the table. I telephoned the club's president. He told me the number was 37. After hanging up I realized that I could not be sure of this figure because I did not know whether the president was a truther or a liar. I then telephoned the club's secretary. "No, no," the secretary said. "Our president, unfortunately, is an unmitigated liar. There were actually 40 men at the table." Which man, if either, should I believe? Suddenly I saw a simple way to resolve the matter. Was it 37 or 40?