Here is the puzzle.  As ever, please do NOT post your answers, but do say if you think you have solved the puzzle and how long it took. Solution on Monday.

Given a sack of sugar, an unbalanced scale, and two 5-pound weights, measure exactly 10 pounds of sugar.

I have produced an ebook containing 101 of the previous Friday Puzzles! It is called PUZZLED and is available for the Kindle (UK here and USA here) and on the iBookstore (UK here in the USA here). You can try 101 of the puzzles for free here.

36 comments

  1. Can we assume the scale is unbalanced by a difference on each side of less than 5 pounds?
    Then it took me 5 seconds, and I can do it with one weight.

    If the unbalance is between 5 pounds and 10 pounds, then I’d need both weights and some extra sugar. Or, a single weight and a lightweight bag or box.

    If the unbalance is greater than 10 pounds, then I’d need both weights and a lightweight bag or box.

  2. Immediate, if I interpet the meaning of “an unbalanced scale” as a scale that is not innaccurate, but just a scale that does not have each dish at the same height when there is nothing on either of them.

  3. Got a sollution (maybe there are more possible). But if the imbalance is bigger than the total weight of the bag of sugar and the weights, it won’t work.

  4. As is clear from several replies, the difficult bit is to know what properties some “unbalanced scales” should be expected to have, as there are several possible faults that could lead scales to be unbalanced. I suspect that the specific property that Richard has in mind is that the scales can be brought back into balance by the addition of a small weight to one side of the scales, and having got them into balance, addition of equal weights to each side will keep them in balance. We do, of course, have the materials with which to verify that these properties apply.

    1. That’s the definition of “unbalanced” I thought of. I assumed the imbalance is relatively small and either (a) there’s a supply of spare sacks / bags or (b) the containers on which you place items to weigh are either dishes or have a rim, arriving at a resolution within a couple of seconds (I won’t say ‘arrived at a solution’, as the obvious way to make a solution would require liquid [as Paul indicates above], which doesn’t appear to be present…)

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