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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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 Can be done in only 4 steps Comment 17 of 17 |
Lets label the weights KJLMN. The measuremnts will be either =,< or >. My first example will show equal measurements;

(1) Weigh K and J, if they are equal then J is either on the right/left of K i.e ( - -J-K- - or - - K-J- -)

(2) Weigh J and M, lets again assume that they are equal then ( - - M-J-K- - or - - - K-J-M- -)

(3) now weigh K and N, again if they are equal then ( - - M-J-K-N- - or - N-K-J-M-)

(4) weigh N and L, and this measurment will determin the above sequence.

Lets now dicuss unqual/equal weights;

(1) Weigh K and J, if J>K then J is on the right of K i.e ( - -K- -J- or - - K- - -J- or -K- - - -J- )

(2) Weigh J and M, if J=M then ( - -K-M-J- - or K - -M-J-....and so forth....

If you follow these steps, you can get many different arrangments and using the steps/logic I mentioned above it is possible to figure this out only in 4 steps! You can apply any different arrangements and it will still be possible to figure it out in 4 steps.
 Posted by Manish on 2005-03-21 06:46:28

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