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?

Um .. try this for a solution.  This is the order, starting at the first one and working around the circle to the last one (which is beside the first one).

1
29
4
25
8
21
12
17
15
18
11
22
7
26
3
30
2
27
6
23
10
19
14
16
13
20
9
24
5
28

1 is opposite 30.
2 is opposite 29.
3 is opposite 28.
etc.
1 has 28 and 29 beside it and therefore 30 has 2 and 3 beside it.
Then 4 is beside 29 with 27 beside 2 and 5 is beside 28 with 26 beside 3.  And keep going to get the above list.  No really sure how I'd prove that it balances the centrifuge though.

Posted by Morgan on 2005-11-14 18:45:58