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(5): Sums of irrationals
Construct the number (5 - Sqrt(2) ) (irrational),
Add Sqrt(2) (irrational), answer 5 (rational).
If you think about it, there are any number of examples any of which may crop up in disguise.
Posted by goFish
on 2005-11-01 15:33:04