Question 857968: given 12 pool balls each identical in shape and colour knowing that one of the pool balls is slightly heavier or lighter than the others, in a three balance scale "weighings" identify the odd pool ball and state whether it is lighter or heavier than the rest
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! First weighing: Split up the balls 50/50 on each side. Place 6 balls on each side. The side that is heavier will stick around while the other 6 balls will be tossed.
Second weighing: The 6 balls that weren't tossed and stick around will be weighed. Again, they'll be split 50/50. So three balls on each side. The heavier side moves onto the next weighing.
Third weighing: Pick any two balls from the heavier side in weighing #2. Weigh them (one ball per side). There are two case scenarios that could happen
Scenario A: If you get a perfectly balanced scale, then the heavier ball is the one that wasn't weighed. This is because if the heavier ball was part of the two weighed, then the scale would tip either way. If it doesn't tip, then the heavier ball is not weighed.
Scenario B: If the scale tips in either direction and it's NOT balanced, then the heavier ball is where the scale tips.
So you can see that just 3 weighings will help find the heavier ball.
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