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 Vuksa)

Just one minor adjustment; it's not three 12-slot, but three 10-slot parts, and the rest is the same. Sorry.

Because the sum of all the samples equals to 465, it's clear we have to divide the cicumference into three 10-slot parts, and each slot has to get 155g of samples. Knowing that, we put them in this order:

1st part - 1, 4, 7, 10, 13, 18, 21, 24, 27, 30 = 155g

2nd part - 2, 5, 8, 11, 14, 17, 20, 23, 26, 29 = 155g

3rd part - 3, 6, 9, 12, 15, 16, 19, 22, 25, 28 = 155g

Posted by Vuksa on 2006-04-06 09:07:22