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Agua and wine

Two glasses, two transfers and a seemingly very simple question. It is one of those riddles that invite you to calculate right away, although the decisive factor does not always come in the longest count.

You have a glass full of water and another full of wine, both with the same amount. You add a tablespoon of water to the glass of wine and mix.

Then you pour a tablespoon of that mixture back into the glass of water. What's more at the end: water in the glass of wine, or wine in the glass of water?

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Hints

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It is not necessary to follow what happens in the mixture drop by drop.
After the two transfers, both glasses once again have the same total volume.

Solution

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Answer: There are exactly the same amount. Explanation: After the first step, the wine glass contains a little water. After the second, the glass of water receives back a mixture that contains some wine. The cleanest way to look at it is this: - at the end, both glasses once again have the same total amount as at the beginning;

therefore, the amount of “foreign” liquid that has entered each glass must exactly compensate the amount of own liquid that has left. If there were more water in the wine glass than wine in the water glass, one of the glasses would necessarily have more “foreign” liquid than the other has lost, and that is impossible since the final total quantities are the same. Put even more simply: the amount of water that ends up in the glass of wine is exactly equal to the amount of wine that ends up in the glass of water.

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