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?

consider each person to be a liar

1 ' the number has 2 digits '
if the number is a divisor of 150, and is not 150, then is must be at most 75, which has 2 digits, therefore 1 cannot be false

2 'the number is a divisor of 150'
it must have 2 digits, cannot be 150, and must be divisible by 25, eg 25, 50 or 75.
unfortunately these are all divisors of 150 therefore 2 must be true

3 'the number is not 150'
if the number is 150 then it cannot have 2 digits, so this must be true as well

4 'the number is divisible by 25'
we need to find a 2 digit number which is a divisor of 150, and is not divisible by 25.

Easy: 10,15 or 30 would do the trick

Also, note that all could be telling the truth, and the line saying one of these people was not telling the truth could be the lie.

Posted by ubergeek on 2002-12-25 22:32:24