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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.)
partial soln | Comment 1 of 5
For N<9 I would want to go first except for N=1 and N=4
My opening move for N=2 is (naturally) to remove 1 object 
My opening move for N=3,5,6,7,8 would be to remove the 
center object for odd N and the center 2 objects for even N.

I should state this more strongly: given my play, I would be guaranteed a win. Against a reasonable player, starting with N=4, I would lose.

I think things may change starting at N>8, but I 
am still working on it... TBC

Edited on December 16, 2021, 11:37 am
  Posted by Steven Lord on 2021-12-16 11:23:48

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