The Game of Tri.

is a familiar example of a Tic-Tac-Toe paper-and-pencil strategy game. Such games help students evaluate alternatives and their consequences. These skills are important mathematical skills as well. Another paper-and-pencil strategy game for two players that can be used to develop these skills is the game of "Tri." To play the game, two players arrange six dots in the shape of a hexagon on a piece of paper. Each player in turn draws a line segment joining two points that are not already joined by a line segment. The moves of each player can be identified by having players use pencils of different colors for drawing their lines. The first player to draw a triangle, all of whose sides are drawn with his color, is a winner. A winning triangle must have three of the original six points as vertices. Unlike Tic-Tac-Toe, in which there is a strategy that forces the game to end in a tie, Tri always has a winner (Harary 1972). The sequence of moves in figure 1 shows that there can be a winner of a nontrivial game as early as the seventh move. Once the players develop a winning strategy for Tri the game can be made more