Challenge Jan-2020

NIM Rules                                                                                 Solutions

Variants of Nim Game have been played since ancient times.  This challenge uses the following version of the game:

There is a number of red balls in the row below (it could be 15, 16, or 17 balls). Two players take turns removing balls from the row, but only 1, 2 or 3 balls at a time. The player who removes the last ball loses.

You may play this game with your kids using pencils or matches. Let’s assume you play against a computer. You need to make decisions who starts the game and how many balls to take after the computer takes its balls. Try to define the rules that provide a winning strategy.

Please submit your rules or complete solution for this game using your favorite BR&DM tools.