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?

I don't think anyone has yet come up with the complete set of Ns that work.  It's such an interesting problem that I'd like to call perplexuser's attention to it again.

I noticed that some people were thinking about this in the wrong way.  Namely, "In order for the centrifuge to balance, each half must weigh equal to the other half, no matter how it is divided" is false.  For a counterexample, look no further than this following balanced centrifuge:

 1 0
0   1
 1 0

That's all I have to say.

Posted by Tristan on 2006-02-03 21:26:57