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There are two bottles each with a capacity of two liters. One bottle contains one liter of water, the other contains one liter of wine. There are two things you can do: (a) pour fluid from either bottle onto the floor, and (b) pour fluid from one bottle into the other. The only constraint is that you must always have at least one liter of fluid in the wine bottle. The object is to dilute the wine in the wine bottle with water as much as possible. What is the maximum dilution you can achieve?. Prove it!.

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If the wine bottle must contain one liter at all times, then you cannot empty anything from the wine bottle. The only solution is to pour the water directly into the wine with the greatest force possible, to expel the wine.

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add 1 drop of water to wine bottle ... shake .. tip out 1 drop from wine bottle.
( this will be almost pure wine) repeat until all water is used.

am i on the right track ?

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Oops, I misread.

Am I able to freeze the water? Then I can get nearly 100% water.

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ooragnak is on the right track.

Do this N times
1. transfer 1/Nth of a liter of water into the wine bottle
2. shake the wine bottle
3. discard 1/Nth of a liter of the mixture in the wine bottle

The remaining liquid will contain (N/(N+1))^N liters of wine. As N approaches infinity, this approaches 1/e. Therefore, you can do no better than 1/e, which is approximately 0.36787944.

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Unless you're allowed to freeze the water.

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Quote:

Do this N times
1. transfer 1/Nth of a liter of water into the wine bottle
2. shake the wine bottle
3. discard 1/Nth of a liter of the mixture in the wine bottle

The remaining liquid will contain (N/(N+1))^N liters of wine. As N approaches infinity, this approaches 1/e. Therefore, you can do no better than 1/e, which is approximately 0.36787944.

Thanks markr...
I always knew that you will be having the answer..

We have some out of the box thinking
SCoates :

Quote:

Unless you're allowed to freeze the water.

But alas, it has been mentioned that

Quote:

There are two things you can do: (a) pour fluid from either bottle onto the floor, and (b) pour fluid from one bottle into the other.

I have one more,

Birbal has got two mobile phones and unfortunately (orr fortunately) he does not know the phone number of any of his mobiles.

Can you help him to find it out????

There is just one condition (only oneohh its so easy then)

You don't have to use/call any third phone (not even customer care).

Question

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Our phones have their numbers stored in them. I assume that's not what you're looking for. I also assume the answer is not to dial all possible numbers until the other one rings.

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markr wrote:

ooragnak is on the right track.

Do this N times
1. transfer 1/Nth of a liter of water into the wine bottle
2. shake the wine bottle
3. discard 1/Nth of a liter of the mixture in the wine bottle

The remaining liquid will contain (N/(N+1))^N liters of wine. As N approaches infinity, this approaches 1/e. Therefore, you can do no better than 1/e, which is approximately 0.36787944.

So, the fist time, N=1, and we pour all the water into the wine, then there is no water left!
Or am I misunderstanding this?

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Pick an N (larger is better), then do N transfers of 1/N each time.

If N=1, there is only one transfer and you get a 50% solution.
If N=2, there are two transfers - half a liter each time - and you get a 44.44% solution
.
.
.

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just look inside the mobile phones.. go into my profile and the number should be in there... Twisted Evil

1 question.....does the mobile phones have bluetooth??

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Answer to the OP's puzzle.
Step 1: Take a credit card and cover the top of the bottle with water.

Step 2: Place the bottle of water, upside down, on the bottle of wine so that the credit card is acting as a barrier between the two bottles.

Step 3: Pull the credit card out just enough so that there is a tiny gap for the two fluids to pass through. Since water is denser than wine it will slowly transfer to the lower bottle and the wine will transfer to higher bottle.

Step 4: Remove the top bottle, again using the credit card to keep the fluid in it. You have now switched the water and wine, acheiving 100% dilution.

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