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.

You could get a dummy sample to make a total of six, and distribute them in every other slot.

Or you could do three samples in say slots 1, 5 and 9. After they're done, you could do the two others in two opposing slots.

Since this is a question in "Shapes", perhaps these pragmatic solutions are not what is/are sought, but they'd help the biochemist anyway.

Posted by Charlie on 2003-10-04 13:45:17