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?
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.
Re: Centrifugal Balance
