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9 replies to this topic

#1 PDR

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Posted 06 January 2008 - 05:26 PM

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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#2 Writersblock

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Posted 08 January 2008 - 04:51 AM

Spoiler for You accomplish it at:

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#3 bonanova

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Posted 08 January 2008 - 10:29 PM

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.
Spoiler for Using floating point arithmetic, I get ...

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#4 spoxjox

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Posted 08 January 2008 - 11:12 PM

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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#5 PDR

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Posted 09 January 2008 - 12:48 AM

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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#6 rookie1ja

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Posted 09 January 2008 - 01:10 AM

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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#7 Writersblock

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Posted 09 January 2008 - 03:24 AM

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

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Posted 09 January 2008 - 02:30 PM

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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#9 bonanova

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Posted 09 January 2008 - 02:33 PM

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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#10 rookie1ja

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Posted 09 January 2008 - 04:55 PM

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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