I am a three digit number.
I am either divisible by 3 or by 5.
I am either divisible by 4 or by 6.
I am either divisible by 5 or by 7.
I am either divisible by 6 or by 8.
I am either divisible by 7 or by 9.
I am either divisible by 9 or by 11.

What am I?

(Note: "divisible" means leaving no remainder.)

462

Logic approach:

From Rule #2, the answer is divisible by 2 (since it is divisible by 4 or 6)
Assume it is divisible by 9:
  Then it is not divisible by 7 (Rule 5)
  Also it is divisible by 3 and thus not divisible by 5. (Rule 1)
  These two statements counterdict Rule 3.
Thus it is not divisible by 9:
  Then it is divisible by 7 and 11 (Rules 5 and 6)
    Then it is not divisible by 5 (Rule 3)
      Then it is divisible by 3 (Rule 1)
  Divisible by 3 and divisible by 2 make it divisible by 6
    Then it is not divisible by 4 or 8 (Rules 2 and 4)

With 3,6,7,11 as factors the LCM is 462. For three digit numbers, the only other multiple that would work is 924. However, this is also divisible by 4, and therefore not a solution.

Edited on May 13, 2006, 11:05 am

Posted by Leming on 2006-05-13 10:46:29