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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.)
Solution Winning Strategy (spoiler) | Comment 7 of 26 |
I believe that the first player can force a win.  

First Player, Move 1: remove just a single counter (any one will do).

First Player, Move 2:  No matter what the 2nd player does, make a play which leaves 4 counters in just two rows or columns.  There are two basic positions (excluding reflections, rotations, transposition of rows, etc.).  They are (a) 4 counters in a 2x2 and (b) 4 counters in a 2x3 or 3x2

  a)  xx         and b) xx
       xx                     xx

First Player, Move 3:  No matter what the 2nd player does, make a play which leaves exactly one stone

  Posted by Steve Herman on 2009-06-25 16:18:07
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