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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(3): tes he can | Comment 12 of 26 |
(In reply to re(2): tes he can by pcbouhid)

This was posted quite late at night (my time) just after I'd emailed Jer about something.

Somewhat startled to find it, I focussed upon 'middle' and was certain that B could always win from A starting thus, just one cell!

In my flurry of diagrams I think I have Ady's model, I certain have such configurations but whether they were built against his description I don't know.  All my investigations suggested that B could always win which is why I may not have probed that scenario properly when I drew it (if I ever did).

I am not going to categorically state that A does not follow the strategy outlined by Ady that B can always provide a winning strategy, but it would seem that way. 

  Posted by brianjn on 2009-06-26 00:50:44

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