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Y-San's centrifuge


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12 replies to this topic

#1 bonanova

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Posted 30 January 2013 - 09:21 PM

In solving a detective case Y-San went to her lab to use her centrifuge.
It has twelve slots, spaced as the hours on a clock. She knows the
importance of filling the slots in a manner that maintains proper
balance, at its high operational speed.

So, she wonders aloud, just loud enough for you to overhear, just how
many different numbers of samples could she process at once and still
maintain that balance?

She of course deduced the answer as quickly as her words were formed,
But she'd love to hear your thoughts on the matter as well.


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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 CaptainEd

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Posted 30 January 2013 - 09:40 PM

Spoiler for It is easy to keep these balanced

Spoiler for of course, she could always


Edited by CaptainEd, 30 January 2013 - 09:46 PM.

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#3 araver

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Posted 30 January 2013 - 10:32 PM

Spoiler for thought

Edited by araver, 30 January 2013 - 10:38 PM.

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#4 bonanova

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Posted 31 January 2013 - 10:58 AM

araver and the Captain are so close.


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

#5 CaptainEd

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Posted 31 January 2013 - 04:14 PM

Araver, I guess that means we don't have it right. So I've got a question for you

Spoiler for can we decompose...


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#6 TimeSpaceLightForce

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Posted 31 January 2013 - 04:25 PM

Araver, I guess that means we don't have it right. So I've got a question for you

Spoiler for can we decompose...

Spoiler for


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#7 TimeSpaceLightForce

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Posted 31 January 2013 - 05:20 PM

 


Araver, I guess that means we don't have it right. So I've got a question for you

Spoiler for can we decompose...

Spoiler for


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#8 CaptainEd

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Posted 31 January 2013 - 05:44 PM

TSLF, I'm glad you responded about the 5 and 7. It made me realize that I didn't fully understand my naive belief that "complementation" should preserve balance. As your example points out, the solution for 7 is NOT the complement of a solution for 5. So I wonder whether, for a larger centrifuge, of size N, the presence of a solution for M samples guarantees the existence of a solution for N-M samples.


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#9 araver

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Posted 31 January 2013 - 05:50 PM

 Araver, I guess that means we don't have it right. So I've got a question for you

Spoiler for can we decompose...

:duh:

Spoiler for

 
The general question still remains ....
Spoiler for

Edited by araver, 31 January 2013 - 05:54 PM.

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#10 CaptainEd

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Posted 31 January 2013 - 06:32 PM

Spoiler for complement of balanced pattern is a balanced pattern

Spoiler for but how to prove that it decomposes into periodic atomic patterns?


Edited by CaptainEd, 31 January 2013 - 06:39 PM.

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