Wizard
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Joined: Oct 14, 2009
November 30th, 2016 at 5:04:25 PM permalink
The king has a barrel full of wine.

On Monday night, a servant steals three cups from the barrel and replaces them with three cups of water.

On Tuesday night another servant steals three cups from the now diluted barrel of wine and replaces them three cups of water.

On Wednesday night yet another servant steals three cups from the now-more diluted barrel of wine and replaces them three cups of water.

On Thursday morning the barrel is 50% wine and 50% water.

How much wine was initially in the barrel?

As always, please put answers and solution in spoiler tags. Free glass of wine to the first correct solution.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
Joeshlabotnik
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November 30th, 2016 at 5:33:37 PM permalink
Quote: Wizard

As always, please put answers and solution in spoiler tags. Free glass of wine to the first correct solution.

Was this at an MGM property? If so, the wine was already diluted before the servants stole it.
Aussie
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November 30th, 2016 at 5:36:45 PM permalink
How do I do spoilers? I might PM you my answer instead. :S
CrystalMath
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November 30th, 2016 at 5:46:30 PM permalink

I heart Crystal Math.
beachbumbabs
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November 30th, 2016 at 5:52:58 PM permalink

"The King has a full barrel of wine".

The barrel was initially 100% wine. Or is that not the question?

3 cups of 100% wine were removed. 3 cups water were then poured in for 100-(3(x%)) purity.

3 cups of 100-(3 (x%)) purity were removed. 3 cups water went in. Wine is now 100-(3 (x%)*y, found similarly. Continue for z. Numerical value left for the math guys.

Or you could be a cook. If 9 cups makes it 50%, 16 cups total also makes it 50% but without losing the wine volume. Add food coloring as necessary. you started with 16 cups.

Sorry, teliot. I'm feeling frisky, but not smart today.

Edit. Rats. My first answer was 15 cups via cook's method. I was closer than I thought. Carry on.

If the House lost every hand, they wouldn't deal the game.
beachbumbabs
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November 30th, 2016 at 5:57:05 PM permalink
Quote: Aussie

How do I do spoilers? I might PM you my answer instead. :S

Quote one of us below to see the format, then cancel the quote. Proceed with your spoiler. It's easy.
If the House lost every hand, they wouldn't deal the game.
onenickelmiracle
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November 30th, 2016 at 6:30:36 PM permalink
I am a robot.
Zourah
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November 30th, 2016 at 7:46:10 PM permalink

I tried to work from the solution backward and I ended up with 86.5% wine or about 15.57 cups of wine out of the 18 cups. If this turns out to be correct I could easily show my work but I saw the other spoiler and it looked more mathematically coherent than what I did!

ThatDonGuy
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Joined: Jun 22, 2011
December 1st, 2016 at 6:45:51 AM permalink
I just saw this one on YouTube, complete with the elegant solution, which I didn't notice.

Let w be the amount of wine (in cups) in the barrel

After the first night, there is now (w - 3) wine in the barrel

On the second night, three cups of (w - 3) / w liquid = 3 (w - 3) / w wine are removed;
the amount of wine is now w - 3 - 3 (w - 3) / w = w - 6 + 9 / w.

On the third night, three cups of (w - 6 + 9 / w) / w liquid = 3 (w - 6 + 9 / w) / w wine are removed;
the amount of wine is now w - 6 + 9 / w - 3 (w - 6 + 9 / w) / w = w - 6 + 9 / w - 3 + 18 / w - 27 / w2
= w - 9 + 27 / w - 27 / w2
Since the barrel is now half wine, this equals w / 2:
w - 9 + 27 / w - 27 / w2 = w / 2
w / 2 - 9 + 27 / w - 27 / w2 = 0
w33 - 18 w2 + 54 w - 54 = 0

Wizard
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December 1st, 2016 at 6:46:22 AM permalink
Aussie and CrystalMath are correct but I also require a solution for the glass of wine.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
ThatDonGuy
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December 1st, 2016 at 6:53:56 AM permalink
Quote: Wizard

Aussie and CrystalMath are correct but I also require a solution for the glass of wine.

Er, what "glass of wine"?
onenickelmiracle
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Joined: Jan 26, 2012
December 1st, 2016 at 7:11:36 AM permalink
Quote: Wizard

How much wine was initially in the barrel?

100%, a barrel full. Winemakers have pride selling to the king. "The king has a barrel full of wine."
I am a robot.
CrystalMath
• Posts: 1911
Joined: May 10, 2011
December 1st, 2016 at 8:47:24 AM permalink
Quote: Wizard

Aussie and CrystalMath are correct but I also require a solution for the glass of wine.

The initial amount of wine is x
The first theft will leave x(1-3/x)
The second theft will leave x(1-3/x)2
The third theft will leave x(1-3/x)3

So, the remaining wine after three days, x/2 = x(1-3/x)3
1/2 = (1-3/x)^3
1-3/x = (1/2)1/3
3/x = 1-(1/2)1/3
x = 3/(1-(1/2)1/3)

Initially, I calculated the amount of water in the barrel, and came up with a polynomial that I couldn't factor.
I heart Crystal Math.
Romes
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December 1st, 2016 at 11:13:42 AM permalink
The king wanted to see who was loyal to him... So he poisoned the wine... So now there's 3 dead servants, and some dead hookers.
Playing it correctly means you've already won.
Wizard
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Joined: Oct 14, 2009
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December 1st, 2016 at 11:29:08 AM permalink
Quote: CrystalMath

The initial amount of wine is x
The first theft will leave x(1-3/x)
The second theft will leave x(1-3/x)2
The third theft will leave x(1-3/x)3

So, the remaining wine after three days, x/2 = x(1-3/x)3
1/2 = (1-3/x)^3
1-3/x = (1/2)1/3
3/x = 1-(1/2)1/3
x = 3/(1-(1/2)1/3)

Initially, I calculated the amount of water in the barrel, and came up with a polynomial that I couldn't factor.

Correct! I owe you one cup of undiluted wine.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)