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Putnam 2002 B4

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March 12, 2012
Putnammodular arithmeticcollege contests

Problem Statement

An integer nn, unknown to you, has been randomly chosen in the interval [1,2002][1,2002] with uniform probability. Your objective is to select nn in an ODD number of guess. After each incorrect guess, you are informed whether nn is higher or lower, and you <spanclass=′latex−bold′>must</span><span class='latex-bold'>must</span> guess an integer on your next turn among the numbers that are still feasibly correct. Show that you have a strategy so that the chance of winning is greater than 23\tfrac{2}{3}.
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