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 re: Solution by Leonidas)

Leonidas,

Actually the moments do balance even on the diagonal suggested by you. The arrangement of the 6 will be as follows:

       1               6

4                               3

       5               2

The the moments will be:

1cos60 + 5cos60 + 4 on one side and
2cos60 + 6cos60 + 3

These 2 are equal because cos60 is 0.5 (I think!! My trig is rusty too.). Hence the centrifuge balances.

Posted by rohit on 2005-10-20 09:12:55