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?

I came to the same solution as Charlie.

The first two TRUE statements (a & b) provides 63 possible numbers. Only 485 provides a unique solution, thus statements #1 and #3 are FALSE.

    1 2 3 4
102 T T T F
132 T T F F
142 F T F F
152 T T T F
162 T T F F
172 F T T F
182 F T T F
192 T T T F
203 F T T F
213 F T F F
243 T T F T
263 F T F F
273 F T T F
283 F F F F
293 F F T F
304 F T F F
314 F T F F
324 T T F F
354 F T F F
364 T T F T
374 F T T F
384 F T F F
394 F T F F
405 T T T F
415 F T F F
425 F T T F
435 F T F F
465 T T F F
475 F T T F
485 F T F T (*)
495 F T F F
506 T T T F
516 T T F F
526 F T T F
536 F T F F
546 F T F F
576 T T F F
586 F T F F
596 F T F F
607 F F T F
617 F F F F
627 F T F F
637 F T T F
647 F F T F
657 F T F F
687 F T T F
697 F T T F
708 F T T F
718 F T F F
728 F T T F
738 T T T F
748 F T T F
758 F T T F
768 F T T F
798 F T F F

Edited on April 21, 2006, 7:18 pm

Posted by Dej Mar on 2006-04-21 19:00:10