Four identical looking objects weigh 3oz, 5oz, 8oz and 11oz. You do not know which objects weigh what and they are too close in weight to tell by holding them. Using a balance scale, how can you determine the weight of each object in only four weighings?
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4$\begingroup$ 3 oz and 11 oz are too close in weight to tell by holding them? Sounds unlikely ... nevertheless, nice puzzle and fun to solve. $\endgroup$– Rand al'ThorSep 18, 2016 at 22:17
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$\begingroup$ Hello Jackson murphy, did you make this puzzle yourself or it is a classic one? Best, Artur $\endgroup$– Puzzle PrimeSep 20, 2016 at 5:44
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2 Answers
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First weigh two of your objects against the other two. Whichever pair is heavier must contain the 11-oz object, since even $11+3>5+8$.
Now you have two objects of which you know one weighs 11 oz. Weigh them against each other to find out which one it is.
Weigh the 11-oz object against two of the remaining three. If the scales balance exactly, those two are 3 and 8 oz. If the 11-oz object is heavier, they are 3 and 5 oz. If the 11-oz object is lighter, they are 5 and 8 oz. Either way, you know the weight of the fourth object.
Now you have only two objects of unknown weight, so you can weigh them against each other to find out which is which.
answered Sep 18, 2016 at 22:16
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5$\begingroup$ It took ye dern near 8 whole minutes... ar' ye getting slew? $\endgroup$– jmbmageSep 18, 2016 at 22:43
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1$\begingroup$ @jmb.mage Aye, gettin' slow in me old age. I kin still take you though, boyo! :-P $\endgroup$ Sep 20, 2016 at 0:01
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Assuming that we have prior knowledge of the weights given without knowing which object weighs what, note that any weighing will always favor the scale pan that contains the 11oz object. This is because the least combined weight of two objects including the 11oz object is
11 + 3 = 14 > (8 + 5) > 13
So, Once the first weighing is completed, the two objects in the pan containing the heavier combination, can be compared in the second weighing, the heavier being the 11oz object.
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1$\begingroup$ You should replace the last > sign by equality. From two measurements you have identified only one weight, the 11oz. However, from the remaining two measurements you might not be able to establish the weights of the remaining three objects, as once you have (with naive comparisons), e.g., a<b and a<c you have no information on whether b>c or b<c. $\endgroup$– MatsmathSep 19, 2016 at 6:44