> Unless I am missing something, this seems really simple. First > weigh: separate the 12 balls into 2 groups of 6. Weigh the 2 > groups. Discard the lighter group of 6. Second weigh: Separate the > remaining 6 balls into 2 groups of 3 balls. Weigh the 2 > groups. Discard the lighter group of 3. Third weigh: Of the 3 balls > remaining, weigh 2 of them separately. If one is heavier than the > other, you have the answer. If they are equal, the one that was not > weighed is the heaviest ball. I haven't heard this problem, so I may > be missing the rules.
You are missing the fact that it is not known whether the ball in question is heavier or lighter than the rest.