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You have three 2-liter jars, call them 1, 2 & 3. Each jar has 1 liter of a different liquid in it - so:

Jar 1 - has liquid A

Jar 2 - has liquid B

Jar 3 - has liquid C.

Your task, pour 1/2 liter from Jar 1 into Jar 2. Now pour 1/2 liter of the mix from Jar 2 to Jar 3. Now pour 1/2 of the mix from Jar 3 back into Jar 1. Assume when you pour, you pour exactly 1/2 liter and the liquid mixes perfectly each time.

Question - how often must you repeat the round of pourings (1 to 2, 2 to 3, 3 back to 1) until each jar holds EXACTLY 1/3 of each of the original liquids?

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Posted · Report post

Pour 49

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Posted · Report post

You have three 2-liter jars, call them 1, 2 & 3. Each jar has 1 liter of a different liquid in it - so:

Jar 1 - has liquid A

Jar 2 - has liquid B

Jar 3 - has liquid C.

Your task, pour 1/2 liter from Jar 1 into Jar 2. Now pour 1/2 liter of the mix from Jar 2 to Jar 3.

Now pour 1/2 of the mix from Jar 3 back into Jar 1.

Assume when you pour, you pour exactly 1/2 liter and the liquid mixes perfectly each time.

Question - how often must you repeat the round of pourings (1 to 2, 2 to 3, 3 back to 1) until each jar holds EXACTLY 1/3 of each of the original liquids?

Clarify: you pour 1/2 liter from Jar3 to Jar1, not 1/2 of Jar3's mix, which would be 3/4 of a liter.

After the 48th pour Jar 1 has exactly 1/3 liter of liquid A

After the 49th pour Jar 2 has exactly 1/3 liter of liquid B

After the 50th pour Jar 3 has exactly 1/3 liter of liquid C

Where "exactly" means within an error bound of about 10**-16, the precision of my processor.

If after some pour the exact conditions obtain, I'd need a different method to find it.

By the way, are we actually counting molecules here? B)

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Posted · Report post

Question - how often must you repeat the round of pourings (1 to 2, 2 to 3, 3 back to 1) until each jar holds EXACTLY 1/3 of each of the original liquids?

Assuming the liquids are treated as ideal, infinitely divisible liquids, my sense is that this will never occur.

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Posted · Report post

Bonova - thanks for the catch - yes I should have said pour 1/2 liter from jar 3 to jar 1. I don't see an edit button on the forum or I'd go back and fix the original... <_<

Assuming the liquids are treated as ideal, infinitely divisible liquids, my sense is that this will never occur.

Agreed. You'll get close, but never hit exactly 1/3 of each in each jar.

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Posted · Report post

I don't see an edit button on the forum or I'd go back and fix the original... <_<

users can edit their posts only within 10 minutes after they post ... so that we can keep track of changes (and nobody is hiding anything)

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Posted · Report post

Yeah, I assumed pouring 1/2 the mix not 1/2 liter.

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Posted · Report post

users can edit their posts only within 10 minutes after they post ... so that we can keep track of changes (and nobody is hiding anything)

That's usually handled automatically by the software, which places an edit history

[last edited on ___ ; ___ edits total]

at the end of the post if another post is made before the edit.

The editor can then append a note saying "Edited to clarify the pouring rules," or some such.

I suppose there is some merit to locking after 10 minutes,

but it does have the drawback of keeping things from being fixed

or, say, withdrawing a spoiler, etc. without forum owner's intervention.

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Posted · Report post

Yeah, I assumed pouring 1/2 the mix not 1/2 liter.

I thought of seeing what happened if you do that.

But if you don't pour 1/2 liter each time, the jars start containing unequal amounts of liquid after a set of pours.

I didn't think there'd be a chance of equal distribution of liquids in that case.

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Posted · Report post

That's usually handled automatically by the software, which places an edit history

[last edited on ___ ; ___ edits total]

at the end of the post if another post is made before the edit.

The editor can then append a note saying "Edited to clarify the pouring rules," or some such.

I suppose there is some merit to locking after 10 minutes,

but it does have the drawback of keeping things from being fixed

or, say, withdrawing a spoiler, etc. without forum owner's intervention.

my experience is that users edited their posts without mentioning what was edited ... thus some next posts were referring to something that was not visible anymore

however, if you feel that enabling editing would not be abused, I might reconsider my attitude ... meanwhile, I could allow the VIP group (bonanova, writersblock, unreality + of course, martini already can edit anything since he is moderator) ... you can pm me or start a new topic to vote for edit or no edit

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