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 similar logic in solving this problem, it can be easily shown that when the numbers (44,3,1,5,2,10,22) in that order are engraved on 7 keys in a  Circular Keyring, the numbers on adjacent groups of keys sum to any value between 1 and 87 inclusively.

Edited on November 14, 2005, 1:51 am

Posted by K Sengupta on 2005-11-14 01:46:47