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12 Identical Balls

A simpler solution would be -- Pick any 6 balls. Divide them into two groups of 3 and weigh them.

If they balance -- mark the set of these 6 balls as OK
If they don't balance -- mark the set of these 6 balls as NOT OK.

-- Now pick 3 balls from the GOOD set and weigh them against 3 balls from the NOT OK set. If they balance -- the ODD one is in the remaining 3 If they don't balance -- the ODD one is in the set of 3 balls that you had picked from the NOT OK set. From this we would also come to know if the ODD ball is heavier or lighter than the rest. Mark this set of 3 balls as ODD

-- From the ODD set of 3 balls, weigh any 2. If they balance, ODD one is the one that's left. If they don't, we can find which one is ODD ( based on the knowledge which we gained previously about the ODD ball being heavy or light)

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