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Steve Martin Inner circle 1119 Posts |
I've got two wine glasses in front of me.
One contains 200ml of red wine. The other contains 200ml of pure water. I take a teaspoon and scoop up 5ml of the red wine, and mix it into the glass of water. I then take the same teaspoon and scoop up 5ml of liquid from the glass of water, and mix that into the glass of wine. Having done that, here is the question: Which is the most "contaminated" glass? In other words - is there now more wine in the glass of water than there is water in the glass of wine, or vice versa?
Any man who reads too much and uses his own brain too little falls into lazy habits of thinking.
Albert Einstein |
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pxs Loyal user London 284 Posts |
They must be identically contaminated
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Steve Martin Inner circle 1119 Posts |
Why do you think that?
Any man who reads too much and uses his own brain too little falls into lazy habits of thinking.
Albert Einstein |
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pxs Loyal user London 284 Posts |
Because after the switching there is still 200ml in both so if one lot is 195ml water and 5ml wine, the other must be 195ml wine and 5ml water
You could work the maths out, but there is no need! |
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Jonathan Townsend Eternal Order Ossining, NY 27297 Posts |
I think they might both taste a bit off. The wine will probably taste less contaminated than the water.
though if you want to be all scientifica about it... wouldn't there be just 5/200 of contamination in the former than the latter? Taste is a funny thing. No disputing taste
...to all the coins I've dropped here
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nike New user ri 50 Posts |
Water in wine?
me thinks in my case the wine would be gone before we could test but ill take a stab no time to do the math, but gut feeling is that the mostly water is more contaminated than the mostly wine the reason being you are moving 100% wine solution to the water glass but you are not moving 100% water solution back to the wine assuming of course the wine and water mix evenly throughout but hey what do I know? |
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0pus Inner circle New Jersey 1739 Posts |
Reminds me of the time I was lost in the wilds of Afganistan.
We lost the corkscrew and had to live on food and water for a week. A harrowing experience! 0pus |
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pxs Loyal user London 284 Posts |
OK - here's the maths
To start, you have A: 200ml wine B: 200ml water First switch A: 195ml wine B: 200ml water; 5ml wine Second switch Take 5ml from B will contain - 5 x (200/205)ml water and 5 x (5/205)ml wine = 4.878ml water and 0.122ml wine So A: 195.122ml wine and 4.878ml water B: 195.122ml water and 4.878ml wine So they are the same |
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Greg Arce Inner circle 6732 Posts |
This reminds me of a strange little example: if you take a spoonful of wine and pour it into a bottle of full of sewage you have sewage... if you take a spoonful of sewage and pour it into a bottle of wine... you have sewage.
Greg
One of my favorite quotes: "A critic is a legless man who teaches running."
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MacGyver Inner circle St. Louis, MO 1419 Posts |
Sewage > everything
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davejesc New user David Juraschek 83 Posts |
What do you guys have against wine that you keep putting stuff in it anyway?
-Dave |
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CWMoss Regular user 111 Posts |
What weighs more....a pound of sewage or a pound of wine?
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nike New user ri 50 Posts |
Ill say a pound of wine
if you drink a pound of water you'll weigh one pound more if you drink a pound of sewage, I'm thinking you will lose some pounds! (depending on what you ate) |
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Jonathan Townsend Eternal Order Ossining, NY 27297 Posts |
Hmmm not happy the pxs wine/water model.
consider this: You have two teaspoons. One goes into the wine and one goes into the water. You pick them up full, at the same time, and carefully bring them over the OTHER container, and pour in the contents. According to the math pxs did, this would yield the same result. For some reason this does not jibe for me. Is there a decimal place error going on here?
...to all the coins I've dropped here
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landmark Inner circle within a triangle 5194 Posts |
If the wine/water set-up is confusing consider this analogous situation which may be easier to think about:
You have one stack of 26 red cards; She has one stack of 26 black cards. Hand her X number of red cards from your stack. She shuffles and hands you back X number of cards from anywhere in her stack. You now have the same number of black cards as she has red cards. You also have the same number of red cards as she has black cards. (Try it out if you don't believe it!) BTW you can repeat this process as often as you like, and still end up with the same result. And of course, Simon Aronson's Shuffle-Bored takes this principle and turns it inside out and upside down. Jack Shalom
Click here to get Gerald Deutsch's Perverse Magic: The First Sixteen Years
All proceeds to Open Heart Magic charity. |
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pxs Loyal user London 284 Posts |
Quote:
On 2004-04-08 11:05, Jonathan Townsend wrote: The analogy is not correct because in your example, you are definitely transferring 5ml of each liquid. In the puzzle as given, however (and in my math calculation), you remove less than 5ml of each liquid. This is because although you initially remove 5ml of wine, when you remove 5ml at the next stage, this is part water/part wine. So less than 5ml of wine is moved. (Ditto for the water - less is moved because some of the 5ml at stage 2 is taken up with wine) I hope that makes sense! |
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landmark Inner circle within a triangle 5194 Posts |
Maybe I'm missing something here, but again, if you look at this with cards, you'll see that you don't even have to make the assumption (as, I believe, pxs does) that the wine and water get mixed thoroughly.
For example, put 5 ml of wine into the water, so: wine glass contains 195 ml of wine, water glass contains 200 ml of water, 5 ml of wine. Now pick up 5ml from the water glass--it doesn't matter what the composition of that 5 ml is! For example, let's say the 5ml consists of 2ml of wine and 3 ml of water. Then we now have: wine glass: 195 + 2 ml of wine =197 ml of wine, plus an additional 3 ml of water water glass: 200-3 ml of water = 197 ml of water, plus 3 ml of wine left over from before. You now have the same amount of wine in the water as water in the wine. In Jon's scenario, if each picked up 5ml in their teaspoons and then switched them, once again there would be the same amount of water in the wine as wine in the water. Hope this makes it more clear. I also hope I'm understanding this puzzle properly! Jack Shalom
Click here to get Gerald Deutsch's Perverse Magic: The First Sixteen Years
All proceeds to Open Heart Magic charity. |
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magicgeorge Inner circle Belfast 4299 Posts |
Your right, Jack, it doesn't mateer if they're mixed thoroughly or not. Pxs' first explanations is the simplest and best. Whatever amount of wine is in the water must be the same amount as the water that's in the wine no matter how they are mixed or transferred.
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C.J. Inner circle There's a lotta rambling in my 2366 Posts |
Ah, sewage cracks me up!
Connor Jacobs - The Thought Sculptor
Mundus vult decipi, ergo decipiatur Be fondly remembered. |
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Samuel Catoe Inner circle South Carolina 1268 Posts |
I understand the mathematical portion of the answers but has anyone considered that the glass of water is the most contaminated. That is my answer. The reason is this:
The water is 100% pure water therefore any addition of any other liquid (wine) will contaminate it with a foreign substance. The wine is 100% wine. Doesn't wine already contain water? Therefore by adding the water/wine substance you will be adding more of what is already present in the glass of wine. This would not contaminate it at all because there are no new ingredients being added. That is my belief.
Author of Illusions of Influence, a treatise on Equivoque.
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