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Water into wine and back

9 replies to this topic

#1 bonanova

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Posted 08 May 2012 - 09:51 AM

A familiar problem concerns two glasses, one containing water, the other wine [edit: in equal amounts]. A certain amount of water is transferred to the wine, and an equal amount of the mixture is transferred back to the water. Is there now more wine in the water glass than there is water in the wine glass? A moment's thought shows the two amounts must be the same.

Is it possible, by thus transferring the same amount of fluid, any number of times, to reach a state where the percentage of wine in each mixture is the same?

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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

#2 Morningstar

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Posted 08 May 2012 - 02:19 PM

Are we assuming that the mixtures are perfectly mixed and that all samples of the mixtures will have the same percentage of each liquid as the entire glass?
Spoiler for Otherwise,

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The cake is a lie.

#3 Barcallica

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Posted 08 May 2012 - 03:54 PM

Spoiler for Not so sure but

Edited by Barcallica, 08 May 2012 - 03:57 PM.

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#4 phil1882

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Posted 08 May 2012 - 05:19 PM

hmmm.
Spoiler for

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#5 bonanova

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Posted 08 May 2012 - 06:21 PM

Are we assuming that the mixtures are perfectly mixed and that all samples of the mixtures will have the same percentage of each liquid as the entire glass?

Spoiler for Otherwise,

Yes. Assume complete mixing.
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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

#6 bonanova

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Posted 08 May 2012 - 06:22 PM

Spoiler for Not so sure but

Yeah, you have it. Nice.
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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

#7 bonanova

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Posted 08 May 2012 - 06:31 PM

hmmm.

Spoiler for

Precisely. Well done.

Spoiler for Interestingly,

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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

#8 Peekay

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Posted 09 May 2012 - 02:50 AM

Spoiler for I think...

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#9 crazy

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Posted 09 May 2012 - 05:56 AM

The question doesnt say that both glasses contain equal volume of liquid.
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#10 bonanova

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Posted 09 May 2012 - 07:39 AM

The question doesnt say that both glasses contain equal volume of liquid.

It should. I've made that edit.
Thanks for making the point.
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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

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