Four people think of a number, and then proceed to each tell you something about it.

• A: The number has 2 digits
• B: The number is a divisor of 150
• C: The number is not 150
• D: The number is divisible by 25

Unfortunately, one of these people is not telling the truth. Who is it?

(In reply to just a thought by Amanda)

You picked the wrong pair to start with.

If B and D are both telling the truth, then the number is 25, 50, 75, or 150, and A and C are either both lying, or are both telling the truth.

But there is one and only one liar, so it must be either B or D.

But A and D together still give 25, 50, and 75, so B would not be lying, so it mus be D. This would be the case if the number were 10, 15, or 30.

Posted by TomM on 2002-10-08 18:56:25