You are given N number of weights that are all powers of 2. You are also given an item that weighs 1003 lbs.

(1) Exactly how many of those weights would be needed to balance the weight of the item if you could only use one of each weight?

(2) What's the fewest number of weights you can use to balance the weight of the item if there is an unlimited amount of each weight available to you?

I agree with some of the earlier posters (as I arrived at their conclusion independently) that the number of weights needed is FOUR - with 2¹⁰ on one side of the scale and (1003, 2⁴, 2² & 2⁰) on the other side.  

Perhaps luvya meant to state "Exactly how many of those weights would be needed to counterbalance the weight of the item...". 

Posted by Dej Mar on 2007-11-10 05:14:15