Math/logic problem?

Here's a simple way to show that they're equal.

When you start, they have the same amount of liquid in each, and when you end, they have the same amount of liquid in each.

Now however much wine was removed from the wine bottle with all things considered had to be EXACTLY replaced by that much water to make the volume the same in the end. So we actually just switched out some wine for the same amount of water.

Answer, again: They're the same.

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Edit to respond to the lots who are saying differently:

Most answers which disagree with me are saying that there is more water in the wine bottle, following some argument about the purity/impurity of the glass of liquid you're moving from one into the other.

Here's the problem with that reasoning:

The amount of wine in the bottle when you pour the "pure" water into it is however much there was in the beginning.

HOWEVER, the amount of water in the water bottle when you pour the "impure" mixture into it is 1 glass less than what we started with, so the impure mixture will actually have more effect on the percentage wine in the water bottle than if it had the full amount in there still.

Think about it - if I pour pure ethanol into a lake, wouldn't I have to dilute it quite a lot to get the same concentration when pouring it into a liter of water?

More water in the wine bottle. It's pretty simple if you can picture it. You take a glass of pure water and put it into the wine bottle. Then, you take a glass of about "half" water and "half" wine from the wine bottle and put it into the water bottle. Therefore, you are actually putting some of the water back into the water bottle. Hence, there is more water in the wine bottle.

more water in the wine bottle .

Because when you take out a glass of liquid from the wine bottle and put it into the water bottle in fact you are taking a mixture of wine and water.

The glass of water you poured into the wine bottle was pure water. The glass you poured into the water bottle was only part wine, since you had water mixed into it. So, you have to have more water in the wine than wine in the water.

Mo is perfectly right,

the volumes at the end are the same,

so you just switched some water with some wine

otherwise the volumes would be different.

It's an old and well known problem

Answer, again: They're the same.

It will have more water than wine in the water bottle and equal proportions of water and wine in wine bottle.

more water in the wine bottle.

the liquid you get out of the wine bottle is a mixture of water and wine, so you are getting less wine in the water bottle.

thus the wine bottle has more water.

more wine in water bottle....just going by simple common sense, where we don't know what is the volume of bottle and how much wine is present in wine bottle.......

In water bottle..there was no wine initially, but after mixing something from wine...it has wine in it and all of it is wine, though in diluted form

more water in the wine

more water in the wine, assuming it mixes thoroughly each time