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
answer by K Sengupta)
(i) Converting 1003 to base 2, we obtain 1111101011.
The total count of 1s is 8.
Accordingly, the 8 weights are:
2^9=512, 2^8=256, 2^7=128, 2^6=64, 2^5=32, 2^3=8, 2^1=2, 2^0=1
(ii) Since two or more copies of the same weight will NEVER produce a new weight, it follows that the available weights will still be the same and, accordingly the total count of available weight is 8.
Explanation to Puzzle Answer
