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 Four Weights (Posted on 2004-07-25)
You have 4 weights weighing 2,3,5 and 7 pounds. The problem is none of them are marked. What is the fewest number of weighings you need using a balance scale figure out which weights are which?

 See The Solution Submitted by Brian Smith Rating: 3.5000 (8 votes)

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 Puzzle Resolution Comment 33 of 33 |

The objective is achieved in terms four weighings as follows:

Weighing I

Take any two of the four given weights and weigh these weights against  the remaining two. The heavier side must contain the 7 pound weight denote the two weights on the lighter side by P and Q.

Weighing II

Weigh the remaining two weights against each other. one of them is now known to be 7 lbs. Denote the lighter of these two weights as R. This will determine which of the two weights is 7.

Weighing III

Weigh P and Q on one side and the 7 lbs weight on the other. the three possible outcomes are:

(i) P+Q< 7; (ii) P+Q> 7; (iii) P+Q = 7

Weighing IV

Weigh P against Q.

If P+Q< 7, then the lighter of P and Q will be 2 while the heavier will  be 3, so that R =5

If P+Q = 7, then the lighter of P and Q will be 3 and the heavier will  be 5 leaving R = 2

If P+Q = 7, then the lighter of P and Q will be 2 and the heavier weight  will be 3, so that R = 3.

Edited on June 18, 2007, 12:23 pm
 Posted by K Sengupta on 2007-06-18 04:55:04

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