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.)

If the number is divisible by 9, then it isn't divisible by 7, then it is divisible by 5, then it isn't divisible by 3, which is absurd.

So, the number isn't divisible by 9, but it is divisible by 11 and 7, and isn't divisible by 5, and is divisible by 3, so it's divisible by 231 (=3x7x11).

The number should be a multiple of 4 or 6, so we must try the even multiples of 231: 462 (which does the job) or 924 (which doesn't, for it's divisible both by 4 and 6).

The answer is 462.

Posted by e.g. on 2006-05-15 07:06:26