Making Ends Meet

making ends meet puzzle

Fifty coins of various denominations are arranged in a row. You will take a coin from either of the row’s ends, then I will, and so on until all the coins are gone. What strategy will ensure that you take at least as much money as I?

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Before you begin, number the coins from 1 to 50 and determine whether the even-numbered or odd-numbered coins yield a higher sum. Because you’re moving first, you can contrive to capture all of those coins. For example, if the even-numbered coins are more valuable, begin by taking coin 50. That forces me to take 1 or 49, which permits you to take 2 or 48, and so on. From Peter Winkler’s excellent book Mathematical Puzzles: A Connoisseur’s Collection, 2004.

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February 27, 2012January 31, 2013 | Puzzles