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?
(In reply to
re: Balancing Act  outside the box by fwaff)
fwaff's solution gives the least number of weights needed if the balance is modified. If the balance is not modified, the answer is four.
Place the 1024 lbs weight on the scale opposite the 1003lbs item, and put 1, 4, and 16 lbs on the same side as the item. Presto! The weight of the item is balanced.

Posted by Bryan
on 20030624 04:41:50 