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Five Weights and a Broken Scale (Posted on 2004-08-02) Difficulty: 4 of 5
You have to sort five weights weighing 51g, 52g, 53g, 54g, and 55g. You have a balance scale with which you can compare the weights. But after solving so many sorting puzzles, it is starting to break down.

If the difference between two weights is greater than 1.5g, the scale will correctly determine which side is heavier. If the difference between the weights is less than 1.5g or equal, the scale will indicate the weights are equal.

Sort the weights in the smallest number of weighings.

See The Solution Submitted by Brian Smith    
Rating: 3.5556 (9 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Some Thoughts re: Inferior alternative | Comment 6 of 17 |
(In reply to Inferior alternative by Penny)

What about 51+55 v/s 52+54? Both are qeual to 106?

Also, in the 3 examples, you have never used 52. You haven't exhaustively covered all the possibilities.

According to me, you can always do the sorting in a maximum of 8 comparisons. Obviously, you may use more, but for a given worst case of selection of weights, you need at most 8 comparisons.


  Posted by dhruv on 2004-08-20 23:35:33

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