bonanova 85 Posted July 16, 2013 Report Share Posted July 16, 2013 Bad thing for a moderator to say, perhaps, but I think this puzzle is worth looking at, even if it may have been posted before. So if you happen to know the answer from a previous posting, let it ride for a few days. There are three pairs of balls - red, white, and blue. In each pair one ball is a little bit heavier than another one. All the heavy balls weigh the same, and all the light balls weigh the same. Also you have a balance scale with exactly three outcomes: <, = and >. You need to identify the three heavy balls. How many times do you need to use the scale? Quote Link to post Share on other sites

0 Solution Yoruichi-san 116 Posted July 16, 2013 Solution Report Share Posted July 16, 2013 BMAD is on the right track, but you can get more info from the first weighing . You can get info on all three colors in the first weighing, which I think is the key. First weigh R1B1 vs R2W2. If "=", R1=W2, B1=R2, so then weigh R1 vs R2 or B1 vs W2 (or B2 vs W1). If "<", R1<R2, B1</=W2 (that's suppose to be 'less than or equal to'), so then weigh B1W2 vs B2W1. If "=", W2>B1. If "<", B1<B2, W1>W2. If ">", B1>B2, W1<W2. Similarly, if ">", R1>R2, B1>/=W2, so then weigh B1W2 vs B2W1. If "=", W2<B1. If "<", B1<B2, W1>W2. If ">", B1>B2, W1<W2. Thanks, bon-chan . Quote Link to post Share on other sites

0 BMAD 65 Posted July 16, 2013 Report Share Posted July 16, 2013 Two weighings Quote Link to post Share on other sites

0 Pickett 13 Posted July 16, 2013 Report Share Posted July 16, 2013 ...to do it in less than 3 weighings. I can find a number of ways to do it in 3, but no less. I'd be interested in hearing how to do it in 2... Quote Link to post Share on other sites

0 DeGe 9 Posted July 16, 2013 Report Share Posted July 16, 2013 3 weighings is rather trivial... just weigh each pair individually and you know which ball is which. Looks impossible with 1. So, I would go with 2 weighings. Quote Link to post Share on other sites

0 BMAD 65 Posted July 16, 2013 Report Share Posted July 16, 2013 (edited) Label the balls R1, R2 B1, B2 and W1, W2 Put R1, B1 on one side, put R2 and B2 on otherside. If They are equal then R1 = B2 since R1 can't equal R2. If they are unequall then R1 = B1 and which ever side is heavier is the heavier pair. Simply test a heavy one with W1 if they are equal then it is heavy, if not, W2 is heavy. Now if they were equal on the previous test, I would then test R1 With R2 vs B2 with W1. Since B2=R1, we are comparing W1 vs r2. If they are the same then r1=w2=b2 otherwise r1=w1=b2. Now that I wrote it out I have found a mistake. My approach will tell me the three balls that go together but it does not tell me which group is heavier necessarilly, in the event I keep getting equalities. So I need too rethink my answer, I think. Edited July 16, 2013 by BMAD Quote Link to post Share on other sites

0 BMAD 65 Posted July 16, 2013 Report Share Posted July 16, 2013 BMAD is on the right track, but you can get more info from the first weighing . You can get info on all three colors in the first weighing, which I think is the key. First weigh R1B1 vs R2W2. If "=", R1=W2, B1=R2, so then weigh R1 vs R2 or B1 vs W2 (or B2 vs W1). If "<", R1<R2, B1</=W2 (that's suppose to be 'less than or equal to'), so then weigh B1W2 vs B2W1. If "=", W2>B1. If "<", B1<B2, W1>W2. If ">", B1>B2, W1<W2. Similarly, if ">", R1>R2, B1>/=W2, so then weigh B1W2 vs B2W1. If "=", W2<B1. If "<", B1<B2, W1>W2. If ">", B1>B2, W1<W2. Thanks, bon-chan . Nice! Quote Link to post Share on other sites

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## bonanova 85

Bad thing for a moderator to say, perhaps, but I think this puzzle is worth looking at,even if it may have been posted before. So if you happen to know the answer froma previous posting, let it ride for a few days.There are three pairs of balls - red, white, and blue.

In each pair one ball is a little bit heavier than another one.

All the heavy balls weigh the same, and all the light balls weigh the same.

Also you have a balance scale with exactly three outcomes:

<,=and>.You need to identify the three heavy balls.

How many times do you need to use the scale?

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