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?

Although I personally would also consider Vina's first balancing as (at least) one weighing, there is something to be said  for your argument "The fewest weighings".

Then you can do it in 2 weighings:  Let 2 + 3 on the left scale and 5 on the right.  It balances.

Take the ball from the right scale, put it on the left scale and take the 3 away, put the fourth ball on the left scale.   Now it balances again: 2 + 5 = 7.

You now know all four. 

Posted by Hugo on 2004-07-27 10:50:56