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?

Name the weights A, B, C and D

First weighing: A+B versus C+D

Second weighing: A+C against B+D

The scale that has 2 times the highest weight must contain the 7 pound weight  (Why are we in pounds / not in Newton?), because all combinations with 7 are higher then any two other weights.  Suppose weighing 1 gives (A+B) > (C+D) and (A+C) > ((B+D), then this gives A = 7 pounds.

Third weighing sets A against (B + D).  Three possibilities. A = (B+D) then A being 7 results in B and D being 2 or 5, this is then solved by comparing them in a 4th weighing. If A > (B+D), then A being 7 results in B and D being 2 or 3, this is then solved by comparing them in a 4th weighing.  If A < (B+D), then A being 7 results in B and D being 3 or 5, this is then solved by comparing them in a 4th weighing.

So my answer is 4 weighings.

I'm trying to solve in in 3 weighings using the 2+3=5 and 5+2=7 balance situations.  Up till now I didn't find a solution. 

Posted by Hugo on 2004-07-25 13:26:55