A merchant has a precision balance scale, set to weigh exact ounces only, to use in case of an apocalyptic electrical failure. What is the maximum number of weights needed to be able to weigh any number of ounces from one through 2000 ounces? What specific weights are they?
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That's more efficient than using 11 powers-of-2 weights: 1, 2, 4, ..., 1024, which was how I first thought to do it. Since you can balance on both sides, there's more freedom.
Brilliant! Thinking out side the box ehh. This technique would work on binary weights too. 2048 on one side, 32 + 16 on the other side.