mathematics - Unknown weight of four identical objects

Four identical looking objects weigh 3oz, 5oz, 8oz and 11oz. You do not know which objects weigh what and they are too close in weight to tell by holding them. Using a balance scale, how can you determine the weight of each object in only four weighings?

Answer

1. 
   

   First weigh two of your objects against the other two. Whichever pair is heavier must contain the 11-oz object, since even $11+3>5+8$.

   
   
   


2. 
   

   Now you have two objects of which you know one weighs 11 oz. Weigh them against each other to find out which one it is.

   
   


3. 
   

   Weigh the 11-oz object against two of the remaining three. If the scales balance exactly, those two are 3 and 8 oz. If the 11-oz object is heavier, they are 3 and 5 oz. If the 11-oz object is lighter, they are 5 and 8 oz. Either way, you know the weight of the fourth object.

   
   


4. 
   

   Now you have only two objects of unknown weight, so you can weigh them against each other to find out which is which.