We want to find strategies to win in various games.  It is possible that there is a systematic way to find such strategies for all games, but we will first explore specific games.

For the first game, you can play against the computer here or against a human here and figure out the rules, or read this:

Chomp
Start with an m by n rectangle.  The 1st player picks a box and remove the boxes above and to the right of it including itself.  The 2nd player does the same.  Repeat until a player is forced to pick the (poison) box in the lower-left corner, in which case he loses.
 

Activity 1

1. Play a few games (start with small rectangle first).  Try different sizes (2 by n, n by n, 3 by 4, etc.)
2. Is there a winning strategy for the 1st player (for special cases)?