Mathematics Problem Of the Week

Spring 2004

POW 12

A Game on a Grid

Let the grid below be the playing board for a game. There are two players, A and B. Player A has red pieces and Player B has black pieces. Each player takes a turn placing a piece on a crossing point of the grid. A player wins by creating a rectangle whose vertices are all of one color. Will there always be a winner? Explain.

Now play the game on boards of various sizes and answer the same question. For example, can we expect a winner if the size of the grid is 4 by 6? What about 5 by 5?

Due Friday, April 23^rd, at Noon.

Solutions should be submitted to Dr. Dan Gagliardi’s mailbox in the Math office or sent via e-mail to dgagliardi@stlawu.edu.

Presentation counts! The prize-winning entry will be selected from all correct submissions, based on the clarity, creativity and elegance of the solution.

Look for the SLU POW on the Web at http://it.stlawu.edu/~math/activities/