Water and Wine
Consider 2 beakers ... one with 10 ounces of water ... and the other with 10 ounces of wine. Begin by transferring 3 ounces of wine into the beaker with water. Alternating back and forth, and stirring thoroughly after each transfer of 3 ounces, how many transfers are necessary for the percentage of wine in each beaker to be equivalent?
posted by Zaux at
8:52 PM
10 Comments:
What is the tolerance for 100% equal?
A previous question said...
"Prove that 0.9999999999..... = 1."
With each pour you will be getting closer to 100%, but you can never reach exactly 100%
Infinite. The percentages of wine/water will asymptotically approach eachother but never reach each other.
To illustrate, the difference in Wine percentages for the first 20 transfers are:
1- 76.92%
2- 53.85%
3- 41.42%
4- 28.99%
5- 22.30%
6- 15.61%
7- 12.01%
8- 8.41%
9- 6.47%
10- 4.53%
11- 3.48%
12- 2.44%
13- 1.87%
14- 1.31%
15- 1.01%
16- 0.71%
17- 0.54%
18- 0.38%
19- 0.29%
20- 0.20%
Cam
They will be the same after the second transfer.
...oooops. Sorry, I misread the question. I suspect the question wasn't posted as it was intended.
Chris,
I hope you find this comment.
It's had no comments lately.
After about 100 pours and stirs, the
percentage of wine to water is 50% to about 16 decimal points.
But what did you suspect the question was at first?
I tried to consider some odd event could happen because when stirring
beaker 2 there would be 13 ounces of liquid, but only 10 ounces of liquid when stirring beaker 1.
Ragknot, I thought it was how many tmes ... to get the percentage of water in the wine to be the same as the percentage of wine in the water.
Theoretically an even number, as that will be the only time that there are equal amounts in the glasses.....but you should never realistically reach this point as Cam says.
But if 0.9999.... can be proven to be 1 mathematically (22nd Dec 09), then anywhere beyond 42 mixes to the 7 decimal places shown on my calculator.
Realistically, at what point would you want to dilute wine? Unless it is a Beaujolais Noveau...
It doesn't have to be an even number. After a while all the wine will be at nearly the same concentration regardless of how much of it is in a given flask.
I did some reading about the 0.999... = 1 proof. The mathematical community agrees with the result.
Well, I had a thought that wine actually contains water. It may contain about 4% alcohol, but I'll bet it probably contains about 80% water. (just an estimate)
I know I said "Never" at the beginning of this ToM.
But I did leave an opening, in that "Mathamatically", even to a thousand decimals they would not be equal.
But as an engineer, I know that "mathmetically" is not always reality. There's something usually an assumption that is not totally correct. At some decimal point you would be splitting molecules, and you can never exactly get 3 ounces, and you can never stir perfectly, so before infinity pours, I think you would reach the reach the point, but there would be little way to tell.
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