A boy met his father after his maths exam. He said, "Dad can you guess the number of students who appeared at our center?"

The following are true regarding the number
a) It has three distinct digits.
b) If you add 99 the number reverses.

He continues saying, "I have the following statements to add regarding the number."

1) It is divisible by the sum of its digits.
2) It is not prime.
3) It has only one common digit with the product of the digits.
4) The sum of the first and last digit is one more than the middle digit.

He adds further that "if I told you which of these statement(s) is/are false then you'd be able to determine the number."

Dad got it. What was the number?

it's 485

let conditions 1) and 3) be false, and it is the only combination of truth values where there is only one solution. Obviously, there are no solutions if you assume all 4 conditions are true, and you can use logical deduction to rule out condition 1) being a possibility. I'm too lazy to explain it..i'll leave it to whoever to verify it.

It's right...

Posted by cyberdan on 2006-04-22 21:10:57