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2020 AMC 10B Problem 16

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2020 AMC 10B Problem 16AMC 10 Step by Step
Name:                             Date: September 13, 2026
Games & Processes · difficulty 3 of 5 · about 3 min · position P16-20

Bela and Jenn play the following game on the closed interval [0,n][0, n] of the real number line, where nn is a fixed integer greater than 44 . They take turns playing, with Bela going first. At his first turn, Bela chooses any real number in the interval [0,n][0, n] . Thereafter, the player whose turn it is chooses a real number that is more than one unit away from all numbers previously chosen by either player. A player unable to choose such a number loses. Using optimal strategy, which player will win the game?

  1. A)

     Bela will always win.\text{ Bela will always win.}

  2. B)

     Jenn will always win.\text{ Jenn will always win.}

  3. C)

     Bela will win if and only if n is odd.\text{ Bela will win if and only if }n \text{ is odd.}

  4. D)

     Jenn will win if and only if n is odd.\text{ Jenn will win if and only if }n \text{ is odd.}

  5. E)

     Jenn will win if and only if n>8.\text { Jenn will win if and only if } n>8.

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