I answered the first part of the questions but I need help filling out the second part.
1. You have six weights. one pair is red, one pair is white, on pair is blue. In each pair one weight is a trifle heavier than the other but otherwise appears to be exactly like its mate. The three heavier weights (one if each color ) all weigh the same. This is also true of the three lighter weights. In two separate weighings on a balance scale, how can you identify which is the heavier of each pair?
what happens if there are twelve weights, and eleven of which are exactly the same and a twelve which is either lighter or heavier than the others but otherwise looks similar. in three weighing on a balance scale, how would I determine which is the different weight and weather it is lighter or heavier?
✅ Answers
? Best Answer
Take the side that weighs heavier. Weigh two against each other. If they match, they are both the heavier of their respective pair. If they do not match, the heavier is the heavy one of its pair and the lighter is the light one of its pair. In this case, you are done, because the third weight is also the heavier of its pair, but if they match, weigh one against the unweighed one to determine if that is the heavier or lighter of its pair.
For example, let’s say you have the pairs like this Rr, Ww, Bb, where the capital letter is the heavy and the lower case is the light one. You weigh one of each, like this.
RWb vs. rwB
The left side is heavier. Take those weights and weigh two.
R vs. b
Here we know that b is the light one of its pair, so the blue one in the other set must be the heavy one.
But let’s say we did R vs W. Since these match, they must both be heavy, and then we only need to know if the blue one is heavy or light.
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I can do it in four, but not three.
Divide the weights into three groups of four weights. Measure two groups against each other. If they match, the off one is in the third group.
Suppose they don’t match. Take two from each group and weigh them. If they match, the problem is in the two you didn’t select. If they don’t match, the problem is in this group. Either way, take one pair and weigh them. Then weigh one in that pair against one known to be right. Either it is off or the other one is.
If the first two groups match, do the same process with the third, unweighed group.