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# Winning a strategic number game

Best Answer Yoruichi-san, 10 June 2013 - 01:57 AM

Spoiler for A lot simpler than it looks...

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Posted 09 June 2013 - 04:07 AM

Alice and Bob play a number game. Starting with a positive integer n, they take turns changing the number with Alice as the first player. Each player in turn may change the number n to a new positive integer k or zero.  either by k -1 or k/2. The person who changes 1 to 0 wins. For instance, when n = 3, the players have no choice, k proceeds from 3 to 2 to 1 to 0, and Alice wins. When n = 4, Alice wins if and only if her first move is to change 4 to 2. For which initial n does Alice have a winning strategy?

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### #2 Yoruichi-san

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Posted 10 June 2013 - 01:57 AM   Best Answer

Spoiler for A lot simpler than it looks...

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Women are definitely stronger. We are [Fe]males, after all...

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