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?

Since on adding 99, the number reverses, the unit's digit must be 1 more than the hundred's digit.

If  the fourth statement is true, the possibilities are-

243, 364, 485.

On knowing which statements are true we can tell what number it is.

So, the first statement should be false.

243 & 364 are divisible by the sum of their digits.

So, 485 is the no. and the second statement is true but the third is false.

Posted by Sparsh on 2006-05-05 10:42:05