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?
(In reply to Answer
by K Sengupta)
The objective is achieved in terms four weighings as follows:
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.
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.
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
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