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Problem of the Week 922

Local Maximum

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You have 55 cards arranged in a circle. On the underside of each card is an arbitrary number, all different from each other and unknown to you. You wish to find a card whose number is larger than the numbers on the two neighboring (adjacent) cards.

What is the fewest number of cards that need to be turned over in order to find such a card? (The choice of which card to turn will depend upon the results of the preceding turns.)

Source: Adapted by Loren Larson (Carleton College) from "Sharygin's Problem" of Alex Bogomolny (www.cut-the-knot.org). Suggested by David Molnar (St. Olaf).
© Copyright 2000 Stan Wagon. Reproduced with permission.

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09 November 2000