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30. Water and Wine

Another old chestnut, but a good one nonetheless.

You have two glasses, one contains water, the other wine. Neither is full but they each contain the same amount of liquid. Tip some of the water into the wine and stir it well. Now tip some of the mixture back so that, once again, the glasses eachcontain the same amount of liquid.

Is there more water in the wine or wine in the water?

Scroll down the page for the answer.

Assume, for example, that each glass contains 90ml of liquid (adherents of the non-metric system will need to think in terms of fluid ounces, or something similar) and that we take 10ml of water and pour it into the wine.

The 'wine' glass now has 100ml of the mixture, ie 90ml of wine plus 10 ml of water.

Now take 10ml of the mixture and pour it back into the glass containing water. Think about this: the 10ml that you take is actually 9ml of wine and 1ml of water.

So the 'wine' glass now has 81ml of wine and 9ml of water.

The 80ml of water now has 9ml of wine and 1ml of water added to it. So it now consists of 81ml water and 9ml wine.

In other words, there is the same amount of water in the wine as there is wine in the water.

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