You start with 24 possibilities. If you halve them each time you will still end up with 3 possibilities after you have used up all 3 weighings.
A straight line is the shortest distance between any two objects unless something is in the way...
What do you mean? That last hint made perfect sense!
Ok, ok, ok. If you can subdivide the possibilities by 3 on each weighing, you could theoretically distinguish between 33=27 different possibilities, which is more than 24.