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?
(In reply to Solution
Alright, I buckled. Here is a proof by counterexample that statement #4 must be true.
If it weren't, then possible solutions could be 384, 435, and 495 (among many others of course). Of these three, none are divisible by the sum of its digits, none are prime, and none share exactly one digit with the product of its digits, so there would be no way for the father to arrive at a conclusion.
So statement #4 must be true, and the solution proceeds as described in my last post.
Posted by tomarken
on 2006-04-21 13:06:24