# Can You Solve The Diluted Wine Puzzle?

## Description

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

http://wp.me/p6aMk-4XP

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

If you like my videos, you can support me at Patreon: http://www.patreon.com/mindyourdecisions

Connect on social media. I update each site when I have a new video or blog post, so you can follow me on whichever method is most convenient for you.

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My Books

"The Joy of Game Theory" shows how you can use math to out-think your competition. (rated 3.9/5 stars on 24 reviews) https://www.amazon.com/gp/product/1500497444

"The Irrationality Illusion: How To Make Smart Decisions And Overcome Bias" is a handbook that explains the many ways we are biased about decision-making and offers techniques to make smart decisions. (rated 5/5 stars on 2 reviews) https://www.amazon.com/gp/product/1523231467/

"Math Puzzles Volume 1" features classic brain teasers and riddles with complete solutions for problems in counting, geometry, probability, and game theory. Volume 1 is rated 4.5/5 stars on 11 reviews. https://www.amazon.com/gp/product/1517421624/

"Math Puzzles Volume 2" is a sequel book with more great problems. (rated 5/5 stars on 3 reviews) https://www.amazon.com/gp/product/1517531624/

"Math Puzzles Volume 3" is the third in the series. (rated 5/5 stars on 3 reviews) https://www.amazon.com/gp/product/1517596351/

"40 Paradoxes in Logic, Probability, and Game Theory" contains thought-provoking and counter-intuitive results. (rated 4.8/5 stars on 9 reviews) https://www.amazon.com/gp/product/1517319307/

"The Best Mental Math Tricks" teaches how you can look like a math genius by solving problems in your head (rated 4.7/5 stars on 3 reviews) https://www.amazon.com/gp/product/150779651X/

"Multiply Numbers By Drawing Lines" This book is a reference guide for my video that has over 1 million views on a geometric method to multiply numbers. (rated 5/5 stars on 2 reviews) https://www.amazon.com/gp/product/1500866148/

*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

http://wp.me/p6aMk-4XP

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

If you like my videos, you can support me at Patreon: http://www.patreon.com/mindyourdecisions

Connect on social media. I update each site when I have a new video or blog post, so you can follow me on whichever method is most convenient for you.

My Blog: http://mindyourdecisions.com/blog/

Twitter: http://twitter.com/preshtalwalkar

Facebook: https://www.facebook.com/pages/Mind-Your-Decisions/168446714965

Google+: https://plus.google.com/108336608566588374147/posts

Pinterest: https://www.pinterest.com/preshtalwalkar/

Tumblr: http://preshtalwalkar.tumblr.com/

Instagram: https://instagram.com/preshtalwalkar/

Patreon: http://www.patreon.com/mindyourdecisions

Newsletter (sent about 2 times a year): http://eepurl.com/KvS0r

My Books

"The Joy of Game Theory" shows how you can use math to out-think your competition. (rated 3.9/5 stars on 24 reviews) https://www.amazon.com/gp/product/1500497444

"The Irrationality Illusion: How To Make Smart Decisions And Overcome Bias" is a handbook that explains the many ways we are biased about decision-making and offers techniques to make smart decisions. (rated 5/5 stars on 2 reviews) https://www.amazon.com/gp/product/1523231467/

"Math Puzzles Volume 1" features classic brain teasers and riddles with complete solutions for problems in counting, geometry, probability, and game theory. Volume 1 is rated 4.5/5 stars on 11 reviews. https://www.amazon.com/gp/product/1517421624/

"Math Puzzles Volume 2" is a sequel book with more great problems. (rated 5/5 stars on 3 reviews) https://www.amazon.com/gp/product/1517531624/

"Math Puzzles Volume 3" is the third in the series. (rated 5/5 stars on 3 reviews) https://www.amazon.com/gp/product/1517596351/

"40 Paradoxes in Logic, Probability, and Game Theory" contains thought-provoking and counter-intuitive results. (rated 4.8/5 stars on 9 reviews) https://www.amazon.com/gp/product/1517319307/

"The Best Mental Math Tricks" teaches how you can look like a math genius by solving problems in your head (rated 4.7/5 stars on 3 reviews) https://www.amazon.com/gp/product/150779651X/

"Multiply Numbers By Drawing Lines" This book is a reference guide for my video that has over 1 million views on a geometric method to multiply numbers. (rated 5/5 stars on 2 reviews) https://www.amazon.com/gp/product/1500866148/

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