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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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 balance? | Comment 13 of 30 |
I think it may come down to arranging the weights such that any selection of half A vs half B will be shown to be equal.

For example, six doesn't work, but here's what I mean.  The arrangement 1 6 3 2 5 4 will always be out of balance 10 vs 11 when splitting the centrifuge along any of the 3 half divisions.

Hmmm.  But each "imbalance" is offset by 120 degrees from every other.   It's too late for me to think too clearly, but perhaps this arrangement would work after all.  6v5, 4v3, and 2v1 all "imbalance" symmetrically and create a balance.  If this is the case, then it should work for any n=2m, m is odd, where you can create these symmetrical imbalances.

 Posted by Bob Smith on 2005-10-22 00:41:04

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