Monday, August 14, 2006

Gin and vermouth

Here is a puzzle from Schelling's book, Micromotives and Macrobehavior:

You have a glass of gin and a glass of vermouth. You lift a tablespoon of gin and pour it into the vermouth. You then take a tablespoon of the liquid in the second glass, vermouth with some gin in it, and transfer it to the first glass. Which is now the greater quantity, vermouth in the gin glass or gin in the vermouth glass?

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  2. Your prize is that you get to see the answer from Schelling's book: We don't know how the mixture was stirred but it doesn't matter. Whatever fraction of the returned spoonful is vermouth, the rest is gin, so the gin left behind occupied the same part of a spoonful as the vermouth carried on the return trip.

  3. An easier way to see the answer is that each glass ends with the same amount of liquid with which it started.