I haven't played a game of Chess in years. I was recently approached by some students asking to start a Chess Club, and we're going ahead with that. I hope I'll be able to learn to play moderately from them!
Yesterday we were set to have another "Game Day" in class where students would find values (and outcome classes) of different game states. I was hoping to do Chess, and had been flipping through Noam Elkies' paper on Chess end games. A lot of stuff in there was excellent and would really get my class thinking.
But I chickened out. I know that most of my students know how Chess works, but I wasn't sure if they'd be able to see some of the acceptable moves quickly. I was nervous teams might spend half the class figuring out what was going on in one example. Worse, I was afraid I wouldn't be able to cook up new examples on the fly as I have the rest of the year. I have to really be careful with Chess to avoid instances that are not short games.
Instead, I introduced Konane (I'll write separately about this game some time; it's very nice). I played a few times with my aide the day before, then threw a bunch of boards up on the whiteboards. The students dove in immediately; writing up outcome classes, values, and questioning or confirming the results of other teams. I stopped every so often to explain how to derive some values and to switch up partners.
So far, we have only covered Nimbers (defined only via equivalence to Nim heaps) and positive and negative integers, so some of the boards were not given explicit values by the students, as expected. It is almost equally rewarding when students express frustration over not knowing the value of Up---I know they're interested to hear more from our lecture days.
We really should do Chess, though. There are only a few more weeks before we get deep into the student presentations, so I'll have to introduce it soon! Hopefully I'll have good news to report then.
A Domino-Covering Problem
3 months ago