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Non-Adaptive 12 Identical Balls

There is no solution to this problem. Let the predetermined pairs of sets of balls to be weighed be (S1,T1), (S2,T2) and (S3,T3). Now each weighing will (independently) determine a set of possible balls B1, B2, B3 which may contain the odd ball. The solution (assuming it exists) will be the single ball which lies in the intersection of B1, B2 and B3. It is key to note that Bj will either be the union of Sj and Tj or the set of of balls that are not in Sj and Tj. In other words each Bj can be one of two possible sets so there are at most 8 values for this intersection. If the odd ball isn't one of these (at most) 8 values then it obviously can't be determined by this weighing process.