Unformatted text preview: m chips between them. You may take one chip from each of two piles and place them in a third pile. Is is always possible to transfer all chips to the same pile? (You may assume n,m ≥ 3.) (b) Start with three piles of chips, distributed in some manner. Your score s is initially zero. You may transfer one chip from any pile with x chips onto any other pile with y chips, and your score changes by s 7→ s + yx + 1. The game ends when the chips return to their original distribution; what is the maximum possible score attainable at this point? (6) Show that for any six disjoint circles of radius one in the plane, the distance between the centers of some pair of them is at least 2 √ 3. 1...
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This document was uploaded on 03/03/2011.
 Fall '09

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