This one will have to be figured out later when I can really concentrate. The best I can do so far is:

Assuming balls are labeled as follows:
A1, A2, A3, A4
B1, B2, B3, B4
C1, C2, C3, C4

and assuming group A and group B are not equal (1st weigh) and group A is heavier than group B, then create two new groups using the first ball from group C in the first new group with one ball from group A and one ball from group B - something like:

well I'm lost! Who could figure out all of the possibilities and know from which group to pick the next ball to weigh depending on whether or not A is heavier than B, etc? A math wizard! That's not me!

I give up!!!! :o)

if not equal, then weigh
>That's the first step. If you weigh A and B and they are equal, that is the simplest of the solutions. The difficult solution is when A is not equal to B.
>
>>I don't know this one either, but does it have something to do with breaking down the balls into 3 groups of 4 balls in each group and then comparing the weights of the each group and going on from there? It seems like mathematically it could be broken down...
>>
>>Tracy
>>
>>>You have 12 billiard balls.
>>>
>>>One of them is either lighter or heavier than the others.
>>>
>>>You can weigh the billiard balls 3 times on a balance scale.
>>>
>>>You need to find out which ball it is and whether it is heaver or lighter.