ABSTRACT
One of the identifying characteristics of the contemporary mathematician seems to be his insatiable curiosity about anything or everything. Anything or everything, that is, which seems to have underlying mathematical principles behind its operation. A group of graduate students at Newark State College, Union, New Jersey, at the suggestion of Gail Koplin, got interested in the game called Dots and Squares (or, sometimes, just Dots). A commercial version of the game is called Square It. This is the game consisting of a square array of points and is customarily played by two people. Each, in turn, connects a pair of points until such time as a square is enclosed. The person enclosing a square places his initials in the square and the game continues until all the squares are claimed by one or the other contestant. Various strategies occur during the game. Sometimes the closing of the fourth side of a square then presents opportunities for the closing of a whole string of squares. Sometimes the sacrifice of one group of squares to the opponent places him in the unenviable position of having to sacrifice a greater number of squares than he received.
