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12 Identical Balls
This seems easy enough. What about something like this
1) Divide balls into 3 equal groups: [1-4] [5-8] [9-12] 2) Weigh each group side by side 3) In case we are looking for lighter ball, two groups of the three will weigh the same one will weigh slightly less. Now we know we are looking for lighter ball. Similar observation of heavier ball. 4) Say [1-4] weighs slightly less than [5-8] and [9-12] 5) Now make [1-4] into 2 groups: [1-2] and [3-4] 6) Pick one that weighs less, then further divide them so that finally you are comparing a ball to another ball side by side, and now you can pick the one that weighs the less.
Similar logic can be followed for heavier ball.context