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(2): Balancing Act - outside the box by Bryan)

I think that the wording of the question is suitably vague such that any of the three answers given so far are correct for a given interpretation....

If any type of balance can be used then the answer is one. I used to work in a butchers where the balance used was of a type where the balance weight slid along the balance lever which effectively moves the fulcrum and the weight was read from the balance lever depending on the equilibrium position.

If one assumes a traditional pan balance and are allowed to put weights in either pan then the answer is four.

If one assumes a traditional pan balance and interprets 'balance the weight' to mean exactly balance the weight, no more, no less, then the answer is eight.

I'm curious to see which interpretation luvya had in mind when composing the problem.

Posted by fwaff on 2003-06-24 22:16:56