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Tea and Wine

You take a spoon of wine from a barrel of wine and put it into your cup of tea. Then you return a spoon of the (non-uniform) mixture of tea and wine from your cup and put it in the barrel. Now you have some foreign substance (wine) in the cup and some foreign substance (tea) in the barrel. Which is larger: the quantity of wine in the cup or the quantity of tea in the barrel?

they are equal

This is pretty counter-intuitive. Two steps take place: 1. You move a spoonful of wine from the barrel to the cup. 2. You move a spoonful of mixture from the cup back to the barrel.

After step 1, there is 1 spoonful of wine in the cup. In step 2, you move x tea into the barrel and (1-x) wine into the barrel. Therefore, in the cup, you have 1-(1-x) = x wine remaining. x = the amount of tea in the barrel.



One intuitive solution is:

The volume of liquid in both the cup and barrel remains the same as the initial state. If the net amounts of tea/wine transferred was not equal, the volumes would be different. Thus they must be equal.



Hmm, that makes sense. I think the hardest part of this solution is intuitively understanding the duality between tea and wine proportions during the second transfer.




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Submitted by
over 9 years ago
Difficulty 4.7 ?

Math logic