An ancient balance was found along with 5 weights.

Objects placed on one side of the balance could be counter-balanced by a weight on the other side of the balance to determine the object's weight. Also, the object and a weight(s) could be placed on one side of the balance and counter balanced to determine its weight, if necessary.

By using only these 5 weights, the ancients were able to determine the weight of objects weighting 1, 2, 3, ..., 120, 121 grams. What are the 5 weights that the archeologists found?

this is a pretty standard result in number theory.

To measure all weight from 1 to M,the answer is generally the sequence of weights from 1,3,9....3^n , where 3^n <=the max weight to be measured .

Here since its 121 we get n=4.

Posted by Anoop on 2003-02-21 07:12:01