Alice and Bob are playing a game in which they successively write down positive integers.
They are given a target value of *n*; the first player to reach that value wins.
Alice begins with the number 1. Players alternate turns. If the current value of
the number is *x*, the player whose turn it is may either write down *x* + 1
or 2*x*. For which values of *n* can Bob force a win?

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Source: IMO Candidate Problems
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The solution will be posted shortly.
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