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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: Centrifugal Balance | Comment 7 of 30 |

It seems to me that the solution is simple...Each slot sits opposite the difference between it and N+1, so 1 is opposite 30, 2 is opposite 29, 3 opposite 28, etc. The following shows pairings if you can imagine it as an arc:

1   2   3   4   5   6   7   8   9   10   11   12   13   14   15

30  29 28 27 26 25 24 23  22 21   20   19   18   17   16

This will work for ANY even N  slots. Consider 6, again as an arc:

1   2   3

6   5   4

Opposite numbers add up to N+1, or 7.

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