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 Five Weights and a Broken Scale (Posted on 2004-08-02)
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)

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 5 weighings is enough | Comment 14 of 17 |

First version (all equal)

1. take 2 weights. if they are equal

2. take one of the 1st wheighing and another, if they are also equal there are 3 consecutive wheights, you know which are on the edges and which is in the middle, however direction is not known (1,2,3; 2,3,4; 3,4,5 or 3,2,1, or 4,3,2, or 5,4,3)

3.take one of the wheights on the edge and one of the remaining wheights, if they are equal, there is a 4-wheights group in series, but without direction (1,2,3,4 or 2,3,4,5 or 4,3,2,1 or 5,4,3,2)

4. take the middle wheight from the second wheighing and the new wheight from the 3rd wheighings to get direction.

5. Wheigh the last wheight with one of the middle wheights finally to decide whether it is 1 or 5.

Edited on October 6, 2004, 8:57 am
 Posted by Detti on 2004-10-06 08:47:14

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