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 Solution by rohit)

I have some questions/doubts
You wrote:
Therefore it is possible to balance any multiple of 6 (including 30).
Therefore it is possible to balance 6n.

Let n = 1 and 2 then I have the following balanced sets:
1 - 4 - 5 - 2 - 3 - 6 and
7 - 10 - 11 - 8 - 11 - 13
How do I have to install the two sets to be balanced ? 

One set after another is VERY unbalanced.

Edited on October 19, 2005, 5:35 pm

Posted by Hugo on 2005-10-19 17:20:14