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<blockquote data-quote="Hypersmurf" data-source="post: 878103" data-attributes="member: 1656">You have to ensure that each ball has a unique three-weigh characteristic - in other words, you can't have any given pair of balls in the same pan in all three weighings.&nbsp; If you know that the scale was always light whenever balls 3 and 7 are together, all you know for sure is that either 3 or 7 is light.So - four balls in each pan, each weighing.First weighing : 1,2,3,4 in pan 1; 5,6,7,8 in pan 2.Second Weighing : 1,2,5,9 in pan 1; 4,8,11,12 in pan 2.Third Weighing: 2,7,8,12 in pan 1; 5,6,10,11 in pan 2.There are twenty-four possible &quot;odd balls&quot; : 1 light; 1 heavy; 2 light; 2 heavy; and so on up to 12 light; 12 heavy.There are twenty-seven theoretically-possible results of your three weighings, depending on whether Scale 1 is balanced, light, or heavy compared to scale 2 :BBB - not actually possible, since we know one ball is weighted.BBL - Ball 10 is heavy.BBH - Ball 10 is light.BLB - Ball 9 is light.BHB - Ball 9 is heavy.LBB - Ball 3 is light.HBB - Ball 3 is heavy.BLL - Ball 11 is heavy.BLH - Ball 12 is heavy.BHL - Ball 12 is light.BHH - Ball 11 is light.LBL - Ball 6 is heavy. LBH - Ball 7 is heavy.HBL - Ball 7 is light.HBH - Ball 6 is light.LLB - Ball 1 is light.LHB - Ball 4 is light.HLB - Ball 4 is heavy.HHB - Ball 1 is heavy.LLL - Ball 2 is light.LLH - Ball 8 is heavy.LHL - Ball 5 is heavy.LHH - not actually possible; no ball is in one tray for weighing 1 and the other for 2 and 3.HLL - not actually possible; no ball is in one tray for weighing 1 and the other for 2 and 3.HLH - Ball 5 is light.HHL - Ball 8 is light.HHH - Ball 2 is heavy.&nbsp;&nbsp; 27 unique states, three of which never occur, leaving 24 - which map to the 24 possible odd balls.-Hyp.</blockquote>

[QUOTE="Hypersmurf, post: 878103, member: 1656"] You have to ensure that each ball has a unique three-weigh characteristic - in other words, you can't have any given pair of balls in the same pan in all three weighings. If you know that the scale was always light whenever balls 3 and 7 are together, all you know for sure is that either 3 or 7 is light. So - four balls in each pan, each weighing. First weighing : 1,2,3,4 in pan 1; 5,6,7,8 in pan 2. Second Weighing : 1,2,5,9 in pan 1; 4,8,11,12 in pan 2. Third Weighing: 2,7,8,12 in pan 1; 5,6,10,11 in pan 2. There are twenty-four possible "odd balls" : 1 light; 1 heavy; 2 light; 2 heavy; and so on up to 12 light; 12 heavy. There are twenty-seven theoretically-possible results of your three weighings, depending on whether Scale 1 is balanced, light, or heavy compared to scale 2 : BBB - not actually possible, since we know one ball is weighted. BBL - Ball 10 is heavy. BBH - Ball 10 is light. BLB - Ball 9 is light. BHB - Ball 9 is heavy. LBB - Ball 3 is light. HBB - Ball 3 is heavy. BLL - Ball 11 is heavy. BLH - Ball 12 is heavy. BHL - Ball 12 is light. BHH - Ball 11 is light. LBL - Ball 6 is heavy. LBH - Ball 7 is heavy. HBL - Ball 7 is light. HBH - Ball 6 is light. LLB - Ball 1 is light. LHB - Ball 4 is light. HLB - Ball 4 is heavy. HHB - Ball 1 is heavy. LLL - Ball 2 is light. LLH - Ball 8 is heavy. LHL - Ball 5 is heavy. LHH - not actually possible; no ball is in one tray for weighing 1 and the other for 2 and 3. HLL - not actually possible; no ball is in one tray for weighing 1 and the other for 2 and 3. HLH - Ball 5 is light. HHL - Ball 8 is light. HHH - Ball 2 is heavy. 27 unique states, three of which never occur, leaving 24 - which map to the 24 possible odd balls. -Hyp. [/QUOTE]

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