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Can You Solve The Diluted Wine Puzzle?

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 Brain Teasers   |   Math
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A servant has a method to steal wine. He removes 3 cups from a barrel of wine and replaces it with 3 cups of water. The next day he wants more wine, so he does the same thing: he removes 3 cups from the same barrel (now with diluted wine) and replaces it with 3 cups of water. The following day he repeats this one more time, so he has drawn 3 times from the same barrel and has poured back 9 cups of water. At this point the barrel is 50% wine and 50% water. How many cups of wine were originally in the barrel? Watch the video for a solution.

*At 4:04 I misspoke. It should be "x minus 9" rather than the spoken words "9 minus x."

My blog post on this video
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Sources
I read this problem in "Famous Puzzles of Great Mathematicians" by Miodrag S. Petkovic.

The puzzle appears in Niccolo Tartaglia's work "General Trattato di Numeri" (1556).

StackExchange has the idea to multiply concentrations
http://puzzling.stackexchange.com/questions/28776/turning-wine-into-water/28781

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