The next games played were variations of Nim. Players removed a variable number of pieces to either try to be the last one to remove a piece, or in another version, force their opponent to remove the last piece. Again, participants shared strategies for winning the games.

Sim Boards were next. We had hexagons with diagonals. Players took turns coloring either a side or a diagonal of the hexagon. The goal is to be the first player to create a triangle. Again, strategies were shared.

After dinner and conversation, we played Chopsticks Rules. The rules are included in the handout link below.

Matt explained some of the logic behind each of the games. He defined what it means to be a solved game. A game might be strongly solved, weakly solved, or ultra-weakly solved based on how well defined the solutions are, assuming optimal playing at each turn. See the photos below for the definitions.

From the new Core Standards for Mathematical Practice, all eight were apparent to some degree!
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.

In the table below, you may click on any image to see a larger version of it. Click the left (return to previous) arrow at the top to return to the page.

Erin introduces her talk.	Participants played tic-tac-toe.	Abdurrahman and Ismail discuss a general solution for tic-tac-toe.
Chris and Silvia playing Nim	Groups played Sim in pairs.	Erin and Matt demonstrate how to play Chopsticks Rule.
Matt explains what it means to have a strongly defined solution, and...	a weakly defined solution, and...	an ultra-weakly defined solution.