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a version of NIM (Posted on 2016-02-04) Difficulty: 3 of 5
Alice and Bob play a game in which they take turns removing stones from a heap that initially has n stones.
The number of stones removed at each turn must be one less than a prime number. Alice goes first.

The winner is the player who takes the last stone.

Prove that there are infinitely many values of n such that Bob has a winning strategy.

No Solution Yet Submitted by Ady TZIDON    
Rating: 3.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re: Mapping out a bit Comment 3 of 3 |
(In reply to Mapping out a bit by Jer)

Well, one reason you could not follow my proof is because I misapplied the Prime Number Theorem.  The number of primes through 10^M is not roughly M/Log(M), it is roughly 10^M/log(10^M) = 10^M/M.  I am fixing my proof up now. 
  Posted by Steve Herman on 2016-02-05 09:53:48

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