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A nim variation (Posted on 2021-12-09) Difficulty: 3 of 5
Nim games are two player strategy games where players take turns removing objects by some rules until none remain.

For this version, place N counters in a row numbered 1 to N.

A player's turn consists of taking either one counter or two counters from consecutive positions.

Whomever takes the last counter loses (this is called a misère game.)

If you were to play this game, for what values of N would you prefer go first and what should be your first move?

No Solution Yet Submitted by Jer    
Rating: 5.0000 (2 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re: game laid out for N<10 | Comment 3 of 5 |
(In reply to game laid out for N<10 by Steven Lord)

Great work.  I only had the solution for 7 when I submitted this.  The furthest I finished was up to 8 and I realized just how complicated this was.  It gets exponentially harder and leads into some unsolved problems.

Thanks for the well laid-out table.  Maybe 1,4,9 are significant because they are squares, but it's probably just the law of small numbers.  I suspect a general rule is out of reach.

  Posted by Jer on 2021-12-23 09:41:13
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