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(2): Solution by Octavarius)
Unless I am missing something, I don't see how this would work
1 4 5 2 3 6 balances, so does
7 10 11 8 9 12
But
1 7 4 10 5 11 2 8 3 9 6 12 doesn't balance at all:
Follow for example the 1 2 diagonal, it has 37 grams on one side and 38 on the other side.
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Posted by Hugo
on 2005-10-20 13:32:27 |
re(3): Solution, I don't think so
