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 Centrifugal Balance II (Posted on 2005-10-18)
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?

 No Solution Yet Submitted by Brian Smith Rating: 4.2857 (7 votes)

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 re(3): Solution, I don't think so | Comment 11 of 30 |
(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.

 Posted by Hugo on 2005-10-20 13:32:27

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