The Price of Wine

[TimeSpaceLightForce]

                                                       

The three boxes were delivered to a store. Each box contains bottles of Regular,Special and Premium quality wines.All of these bottled wines are indistinguishable. Same in bottle and cork shape or color or volume content.Neither sniffing and sipping helps..while allowed to drink. The products only differ in densities. The Regular and Premium weighs X-grams lighter and X-grams heavier from the Special respectively. 1) What must be done to label at least one box correctly using a balance scale in first try?  

[gavinksong]

weigh two bottles from one box against one each from the other two. The three possible outcomes - lighter/equal/heavier tell you which type they are. Example: the densities are 3 4 5. 3+3 < 4+5. 4+4 = 3+5. 5+5 > 3+4.

 

Close, but TSLF said that there can be only one bottle in each pan.

I'm going to have to steal the correct answer from you.

 

Take two bottles from two different boxes. Drink exactly half of one bottle and then fill it back up with the other wine. Then, weigh this bottle against a bottle from the remaining box.

[TimeSpaceLightForce]

.. with one bottle in each pan?

[bonanova]

weigh two bottles from one box against one each from the other two.

The three possible outcomes - lighter/equal/heavier tell you which type they are.

Example: the densities are 3 4 5.

3+3 < 4+5.

4+4 = 3+5.

5+5 > 3+4.

[bonanova]

Much more satisfying, as well! Good one.