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3x3 Nim (Posted on 2009-06-25) Difficulty: 3 of 5
A 3x3 array of counters is laid out. Players take turns removing counters. The rule for removing counters is to pick a row or column and take any 1,2 or 3 from it. Whoever removes the last counter wins.

Does the first or second player have a winning strategy?
What is this strategy?

See The Solution Submitted by Jer    
Rating: 4.0000 (7 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re(2): Winning Strategy (spoiler) | Comment 11 of 26 |
(In reply to re: Winning Strategy (spoiler) by Charlie)

Charlie:


As Jer has pointed out, I have solved the wrong problem.

However, just for the sake of argument, let's say that the objective is to avoid taking the last stone.

If player 2 leaves

  1
  4  6
  789

or

  1  3
  4  
  789 


Then player 1 wins by removing counters 7 and 8, leaving

  1
  4   6
       9

or

  1   3
  4  
       9 

Although I may not have been clear,  these are all variations (via rotation and transposition) of 4 stones in a 2X3 grid.  From either of these positions, player 1 can always force player 2 to take the last stone.

  Posted by Steve Herman on 2009-06-25 21:55:12
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