Department of Mathematics and Computer Science
Friday, October 19, 2012, 4:00
COLLOQUIUM
Speaker: Keith Wolcott
(joint work with Ira Rosenholtz)
Old Main 2231
Tic-Tac-Toe on Topological Surfaces:
Does O always win?
Abstract: Among the various versions of Tic-Tac-Toe, we address the version that is played
on an m × n board where X plays first, followed by O with play alternating, where the first
player that gets three in a row loses (three in a row winning is trivial on larger boards). We
consider boards which are a plane, cylinder, Möbius band, torus, Klein bottle, and projective
plane. O draws or loses on all 3 × 3 boards, but we prove that O wins on all larger boards up
through 6 × 6 and prove that O wins on many infinite classes of larger boards. We conjecture
that O wins on all larger boards. This talk will be quite accessible to a general audience.
Homework: Who wins, with best play on the following board? A draw is pictured.
Figure 1: 8 × 8 Torus Board
SNACKS IN FACULTY LOUNGE AT 3:30 PM.
EVERYONE WELCOME (EVEN IF YOU ARE UNABLE TO ATTEND THE TALK)