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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: Winning Strategy (spoiler) | Comment 9 of 26 |
(In reply to Winning Strategy (spoiler) by Steve Herman)

Say the first player has taken the center piece. Then the second player can take a corner and an adjacent mid-edge piece, leaving, say,


*
* *
***

from which it's impossible to leave one of the two configurations given.

The same configuration is available to the second player if the first has chosen to remove a corner piece.

If the first player's chosen first piece to remove is the center of an edge, then the second player can leave

* *
*
***

and again the first player can't put it into one of the shown configurations.

  Posted by Charlie on 2009-06-25 17:05:26
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