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 Vuksa)

And, thinking a little more about the whole balancing bit... The order of placing would be, starting with the first slot, and completing full circle: 1, 18, 4, 21, 7, 24, 10, 27, 13, 30 (that's the first third), 2, 17, 5, 20, 8, 23, 11, 26, 14, 29 (second third), 3, 16, 6, 19, 9, 22, 12, 25, 15, 28 (third third).

Then we take a look at the slots in pairs, first pair in the first third (1g and 18g) is equal to the first pair in the second third (2g and 17g) and first pair in the third third (3g and 16g). The next pair in the first third is again as heavy as the ones in the second and third thirds (4g and 21g - 5g and 20g - 6g and 19g), and so on.

If this doesn't balance it, then the centrifuge is uneven :)

Posted by Vuksa on 2006-04-10 08:52:02