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# Divisor Take-Away Game

Started by BMAD, Jul 30 2013 01:26 AM

4 replies to this topic

### #1

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.

### #2

Posted 30 July 2013 - 03:21 AM Best Answer

Spoiler for

### #3

Posted 30 July 2013 - 03:50 AM

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

### #4

Posted 30 July 2013 - 04:18 AM

Rainman is a sniper!

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

### #5

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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