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Say I only want to know the heaviest. If I have a balancing scale, that will require N-1 balancing scale.

If I want to know the lightest.

Same.

What about if I want to know both the heaviest and lightest?

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Related question: math.stackexchange.com/questions/1601/… I think of the notes linked from there answers your question as well; if someone looks over them they may post an answer. –  ShreevatsaR Nov 8 '12 at 4:30
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