Last week, in an effort to relive my success with finding negative games by summing to zero, I tried the same thing with a new game. The plan was to add states of a new game to states of games we had already covered, then see if they sum to zero. I wrote up states of the new game, and challenged students to find states in Clobber, Amazons, Nim, etc, that summed with the original game to get zero. Unfortunately, I hadn't had a good idea for a new game, so instead I decided we would play Misere Clobber.
Pretty quickly, students asked me: "Wait, how do we add a normal play game to a misere game?"
Somehow I did some quick thinking (I usually can never seem to do this in front of a class) and reminded myself of how to make this "legitimate". I wound up writing two options on the board:
Either players are not allowed to make the last play in the misere game, or whenever a player makes the last move in the misere game, they immediately lose.
Whew! Things progressed pretty nicely at that point. Still, I was wary of teaching them that games can have the misere property instead of attaching that property to the method for playing a game. At least this took care of covering all the mechanics we needed to find negative games.
I took a number of wonderful pictures of the boards and of my students playing, but my new phone seems to have trouble with its camera and the pictures were never stored. Instead, enjoy these pictures one of my art-minded students drew on my whiteboard after we covered the definition of a game negative. :)
A Domino-Covering Problem
2 weeks ago