My 10-year-old son introduced me to the following variation on nim. Instead of allowing the players to take any number of counters from a pile on a turn, the counters in each pile are arranged linearly, and then you can only remove A CONTIGUOUS BLOCK of counters. Here contiguous means no empty spaces, too. I am also talking about normal play, not misere play here, so that the person who takes the last block and empties the piles, wins.
I don't know a general strategy for this game. Does anyone know if it has been studied?
this game is equivalent to nim, having the same winning positions, though it has additional winning moves. the proof is fairly easy, relying on the fact that the nim sum of two nimbers is never more than the sum of the corresponding numbers. (much) more info can be found from "winning ways" by berlekamp, conway, and guy. erich