We were in our local pub, the Jolly Quizmaster, a while ago, having a restorative pint after a hard day writing some Quiz questions. A strange man approached us and handed us a sheet of paper, on which was written:
- I've got ten or more daughters
- I've got fewer than ten daughters
- I've got at least one daughter
He then said "Only one of these statements is true. How many daughters do I have?"
How many daughters does the strange man have?
Statement 2 is true if the man has no daughters, one daughter, etc. up to nine daughters.
And statement 1 is true if the man has ten daughters, eleven daughters, etc.
So one, and only one, of statements 1 and 2 is always true. Therefore for the number of daughters the strange man has, one or other of these must be the only true statement.
Thus, for only one of the three statements to be true, statement 3 must be false. That is, he does not have at least one daughter - he has none.