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?

Like the old Centrifugal Balance problem, using the sine of the angle it is from the X axis gives the X torque, and angle from Y gives the Y torque. If there was a way to express sin(x/2pi) exactly so it could be solved that would be a good idea, but I haven't found such a solution.

Posted by Gamer on 2005-10-18 20:57:28