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water problem

In the wine/water mixing problem, one starts with two barrels, one holding wine and the other an equal volume of water. A cup of wine is taken from the wine barrel and added to the water. A cup of the wine/water mixture is then returned to the wine barrel, so that the volumes in the barrels are again equal. The question is then posed—which of the two mixtures is purer? The answer is that the mixtures will be of equal purity. The solution still applies no matter how many cups of any sizes and compositions are exchanged, or how little or much stirring at any point in time is done to any barrel, as long as at the end each barrel has the same amount of liquid.
The problem can be solved with logic and without resorting to computation. It is not necessary to state the volumes of wine and water, as long as they are equal. The volume of the cup is irrelevant, as is any stirring of the mixtures.

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