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Y-San's centrifuge

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#11 bonanova



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Posted 31 January 2013 - 06:40 PM

I think you've collectively touched all the bases.


Spoiler for your combined summary, if I may

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#12 CaptainEd


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Posted 31 January 2013 - 06:45 PM

And Nice Puzzle to you, again and forever!

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#13 araver


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Posted 02 February 2013 - 02:13 PM

One final take on the "special" cases missed in the first solve and TSLF's correct scenarios.

Spoiler for

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.

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

Spoiler for so...

And for the more general case:
Spoiler for Not sure,but

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