Engrave numbers on 5 keys on a circular keyring so that the numbers on adjacent groups of keys sum to any value between 1 and 21 inclusively.

For example, 1,1,3,6,6 can sum up to any number between 1 and 17 (1=1, 1+1=2, 3=3, 3+1=4, 3+1+1=5, 6=6, 6+1=7, 6+1+1=8, 6+3=9, 6+3+1=10, etc).

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

Posted by K Sengupta on 2005-11-14 01:42:06