You are a biochemist, working with a 12-slot centrifuge. This is a gadget that has 12 equally spaced slots around a central axis, in which you can place chemical samples you want separated. The slots on the centrifuge are numbered 1 through 12 clockwise (and clock-like).

           12  1
        11        2

      10            3
             °
       9            4

         8        5
            7  6

When the machine is turned on, the samples whirl around the central axis and do their thing. To ensure that the centrifuge runs smoothly, the samples must be distributed in the 12 slots such that it is balanced evenly.

Can you use the centrifuge to run 5 samples?

For example, if you have four samples, they may be placed in slots 1, 4, 7, and 10 to balance the centrifuge.

1 or 11(12-1) are the only number of samples that need to be balanced with water. All sample sizes > 6 can be reached by inverting full for empty possitions of the paterns < 6.

Posted by Dan Porter on 2004-01-13 22:20:35