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?

(In reply to You can get very close, but... by Rollercoaster)

your computational precision limit is reached.

I have revised my opinion on this.  I was getting imbalances when combining groups of six.  I have reached the conclusion that this was due to numerical computational limits on my machine.

Solving algebraically, the whole does balance.

This makes sense since you are adding five groups of 6 with a zero vector sum to an already balanced set.

Posted by goFish on 2005-11-01 15:39:36