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?

(1)
The answer is easily solved by converting 1003 into a binary number. That number is:

1111101011

There are 8 1's, corresponding to:
512, 256, 128, 64, 32, 8, 2, 1. The answer is 8.

(2)
This answer is only different from the answer to (1) when some of the eight weights can be "combined" to equal a new available weight. Since this is not possible, the answer is the same as (1): 8.

Posted by Roger on 2003-06-23 15:11:09