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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.)
re: Inferior alternative | Comment 4 of 17 |
(In reply to Inferior alternative by Penny)

Explaining my previous post (the follow-up post to the first):

First weigh a+b against c+d and also a+c against b+e.

Look up the results in the table under the columns headed ab over cd and ac over be (the two pans are listed vertically rather than horizontally, and the + is not shown). The ^ indicates the top pair is showing lighter than the bottom pair; the v indicates the opposite and the = indicates an equal balance within the inaccuracy of the broken scale.

Then use the four other weighings shown in that section of the table.  Their results uniquely identify the sequence of the weights shown at the left on the given line that matches all 6 results.

  Posted by Charlie on 2004-08-03 08:52:50
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