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You have two equal glasses. One is filled with water. One is filled with wine.

Now you take a spoonful from the water glass, put it into the wine glass, and stir until it is well mixed. Then you take a spoonful from the wine glass, put it into the water glass.

Now, is there more water in the wine glass than wine in the water glass?

(Please note: I am not a molecular physicist.)

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  • $\begingroup$ Although this question is technically a duplicate, I like this way of asking the question, as it is much easier imagining the mixing of wine and water than picturing the mixing and shaking up of two different sand colors. $\endgroup$
    – IQAndreas
    Oct 27, 2014 at 13:30
  • $\begingroup$ @IQAndreas, this way it has second answer, since there is always water in a "pure" wine. $\endgroup$
    – klm123
    Oct 29, 2014 at 8:22

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Counter-intuitively, there are exactly equal amounts. We can see this if we consider that each glass has lost and gained the same amount of liquid (a spoonful), so any loss to the other glass is precisely offset by gain from that glass.

Unless, of course, the "filled with water/wine" statements were to be taken literally, in which case the water glass will have more wine because the wine glass lost some when it overflowed.

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    $\begingroup$ And a drop of liquid will certainly remain on the spoon. Mostly wine. $\endgroup$
    – Florian F
    Oct 27, 2014 at 9:51
  • $\begingroup$ We can dodge that by noting the spoon was never specifically removed. ;-) $\endgroup$
    – frodoskywalker
    Oct 27, 2014 at 10:11
  • $\begingroup$ If we want to get really silly, we'll note that the surface tension of water is higher than that of wine so the spoonful of water would contain more liquid than the spoonful of wine. $\endgroup$
    – frodoskywalker
    Oct 27, 2014 at 10:16
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    $\begingroup$ And, and, what about evaporation? Alcohol evaporates faster. $\endgroup$
    – Florian F
    Oct 27, 2014 at 10:22
  • $\begingroup$ @FlorianF you beat me to it. I'd just posted that :P then saw your comment appear when I hit Add Comment $\endgroup$
    – Joe
    Oct 27, 2014 at 10:27

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