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.

We have 5 samples which we devide in 2 groups: the first group contains 2 stamples and the second contains 3 stamples.Now, we think how to balance the elements of one group (if the elements of one group balance each other, then all 5 stamples will be balanced).
For example: 1)stamples placed in slots 1 and 7 are balanced and stamples placed in slots 2,6 and 10 are balanced. So, we place the stamples in slots 1,2,6,7 and 10 to balanced the centrifuge.
2)2,3,7,8,11;
3)3,4,8,9,12;
4)4,5,9,10,1;
5)5,6,10,11,2;
6)6,7,11,12,3;
7)7,8,12,1,4;
8)8,9,1,2,5;
9)9,10,2,3,6;
10)10,11,3,4,7;
11)11,12,4,5,8;
12)12,1,5,6,9;
(all the solutions form 2 to 12 are obtained by rotating the solution 1)

Posted by Ruxi on 2003-10-06 15:07:03