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