The Many Faces of Tic-Tac-Toe is the fourth book in the series Developing Mathematical Thinking Through Game-based Learning. The connections between the games and puzzles in Tic-Tac-Toe and mathematical thinking are pointed out or left for you to discover in the process of solving puzzles. The Many Faces of Tic-Tac-Toe is intended for a variety of audiences from ages 5 to 90+.
The first four chapters of The Many Faces of Tic-Tac-Toe introduce the basic game of Tic-Tac-Toe and then introduces simple changes to the rules and to the size of the playing board, giving us Reverse Tic-Tac-Toe, Three in a Row Tic-Tac-Toe on a 4x4 board, and Four in a Row Tic-Tac-Toe on larger boards. These basic variations of the classic Tic-Tac-Toe game introduce the important idea of looking at what happens when a rule is changed in a system. This is what we often do in mathematical problem solving and what we often do in mathematical proof.
Chapter 8 introduces 3D Tic-Tac-Toe. This is helpful in developing spatial reasoning and is a great introduction to graphing with three-dimensional coordinates. Chapter 11, Tic-Tac-Square, is another version with an immediate application to school mathematics.
Sample Puzzles from Tic-Tac-Toe
The two games below are games of four-in-a-row tic-tac-toe on 5x5 boards.
7. 8.
7. Where should X play to guarantee a win for X?
8. O just played at a3. Explain why that is a mistake. Where should O have played?
Tic-Tac-Square
The game of Tic-Tac-Square is another variation on Tic-Tac-Toe. Instead of trying to get your X’s or O’s collinear, the object is to get your X’s or O’s arranged at the vertices of a square in a square grid. The two games below are games of Tic-Tac -Square on 5x5 boards.
4. 5.
Tic-Tac-Twice
Tic-Tac-Twice was invented by Andrzej Ehrenfeucht and Pat Baggett and is available as a commercial game distributed by Aristoplay. It is played on two 4x4 boards. Players take alternate turns by placing a colored token (a checker) on an empty spot on one board. At the same move the player puts a token of his/her color on the same lettered square on a second board. You win the game by having four of your colored tokens in a row (horizontally, vertically, or diagonally on either one or the other of the boards). The two boards below show a game of Tic-Tac-Twice in progress. It is the dark checker’s turn. What letter square should the dark checker play next to guarantee a win on his/her next turn?
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