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Guest Message by DevFuse

# Divisor Take-Away Game

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Posted 30 July 2013 - 01:26 AM

Here's the game: the first player picks an integer n > 1 , then the second player subtracts a proper divisor d < n of that number, telling the first player the difference n - d , then the first player subtracts a proper divisor of that new number, etc. The player who announces a difference of 1 is the winner.  Does either player have a winning strategy? If not explain why not; if so, which player is it, does it depend on n, and what's the strategy?

note: A positive proper divisor is a positive divisor of a number n, excluding n itself. For example, 1, 2, and 3 are positive proper divisors of 6, but 6 itself is not.

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### #2 Rainman

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Posted 30 July 2013 - 03:21 AM   Best Answer

Spoiler for

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Posted 30 July 2013 - 03:50 AM

What if player 2 picks their own number and chooses d?

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### #4 gavinksong

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Posted 30 July 2013 - 04:18 AM

Rainman is a sniper!

Edited by gavinksong, 30 July 2013 - 04:18 AM.

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### #5 plasmid

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Posted 31 July 2013 - 02:26 PM

Spoiler for What would happen if the game starts with number N

Edited by plasmid, 31 July 2013 - 02:31 PM.

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