Using a permutation of (1,2,3) we can obtain any sum from 1 to 6. Adding 5 in the above set , we can obtain any sum from 1 to 11. In compliance with the terms of the problem, the order of the 4 Keyrings would be (3,1,5,2). Adding 10 to the rightmost member of the set , we obtain (3,1,5,2,10) which is in conformity with the provisions of the problem under reference.

*Edited on ***November 14, 2005, 1:50 am**