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 Centrifugal Balance II (Posted on 2005-10-18)
A circular centrifuge has 30 slots spaced evenly around its circumference. Thirty samples need to be spun in the centrifuge, their masses being 1g, 2g, 3g, . . . 29g, 30g. How can all the samples be placed in the centrifuge at once while keeping it balanced properly?

For what other values of N is it possible to balance an N slot centrifuge with samples weighing 1g, 2g, 3g, . . . (N-1)g, Ng?

 No Solution Yet Submitted by Brian Smith Rating: 4.2857 (7 votes)

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 re: You can get very close, but... | Comment 21 of 30 |
(In reply to You can get very close, but... by Rollercoaster)

As a follow-up, I did verify that this "close" solution does indeed balance completely by simply summing moments about any arbitrary cross-cut (thanks goFish).

It seems that 10 slots will work as well, with the sequence:

1,10,7,6,3,2,9,8,5,4

And 6 does work with:

1,6,3,2,5,4

With the little algorithm I used, I couldn't get 4, 8, or 12 to work.  My supposition is that it can be balanced for 4N+2 (N=1,2,3...), but perhaps there is another arrangement different than mine that will allow others.

 Posted by Rollercoaster on 2005-11-01 16:25:57

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