Game and Graphs
Fascinating mathematics can arise out of games. This talk will focus on several ``impartial'' games (in which players have identical options) and on the spatial games Hex and Bridg-it. In each case, interesting connections with the mathematics of graphs will be developed. Two examples follow; others will be discussed at the talk, and everyone will have time to analyze (and perhaps even play) several different games.
An impartial game:
Players alternate moving a single queen on a chessboard; on their turn they can move the queen any number of squares to the north, or east, or on a northeast diagonal. The winner is the person who places the queen in the northeast corner of the board. If you are going to move first, what are all initial squares of the chessboard from which you can force a win?
Bridg-it:
On the diagram below, player NS can connect two adjacent #'s with a line segment. Player EW can connect two adjacent *'s. No line segments are allowed to cross. The player to connect their two sides win. If NS goes first, what move can NS make to guarantee a win?
# # # # #
* * * * * *
# # # # #
* * * * * *
# # # # #
* * * * * *
# # # # #
* * * * * *
# # # # #