Game: Avoid Three, or Tic-Tac-No!

Math concepts: slope, logical strategy
Number of players: 2 or more
Equipment: 4×4 or larger grid, pebbles or other tokens to mark squares

Set up

Alexandria Jones and her brother Leon played Avoid Three with pebbles on a grid scratched in the sand, but you can also use pencils or markers on graph paper. You need a rectangular playing area at least 4×4 squares large. The bigger your grid, the longer your game.

How to play

• Take turns placing a pebble or dot in one of the grid squares. But don’t let your pebble line up with any two others. If you put the 3rd stone in any straight line — vertical, horizontal, or diagonal — you lose.
• Beware: many lines are not obvious. For one thing, the pebble squares do not have to be touching to be in line. Think of a chess knight moving steadily southeast across the board. The squares that he would land on form a straight line.
• Also, pebbles do not have to be evenly spaced to make a line. See the example above for two lines that are quite easy to miss.
• Use a ruler or other straight edge to test any disputed lines. If you can place the ruler so that it touches the top right corners of all three squares, those squares are in line (assuming your grid is reasonably even). Or count off the slope: If you move consistently over-and-up, over-and-up, over-and-up — the same amount over and the same amount up each time, like a drunken chess knight who has forgotten his normal move — then the squares you land on are all in line.

Endgame

• When a player makes a line of three or more pebbles, he is out of the game. If a line is not noticed before the next person plays, however, it doesn’t count.
• The last player remaining wins the game.

Comments

Avoid Three is a “poison” variation of traditional tic-tac-toe, which means the situation that would win the normal game instead becomes the losing move. I don’t know who invented the game, but I first encountered it in Mathematical Activities by Brian Bolt, one of my favorite resources for math club activity ideas. If you host a math club or teach middle-school-or-older students, I highly recommend any of the books in this series:

Mathematical Activities: A Resource Book for Teachers
More than 150 games, puzzles and investigations to delight anyone interested in mathematics, together with a commentary which provides solutions and additional ideas.

More Mathematical Activities: A Resource Book for Teachers
127 problems, puzzles, games, and practical activities designed to stimulate spatial thinking, appreciation of numbers, and general mathematical thinking.

Even More Mathematical Activities
A further 133 puzzles, investigations, games, projects and applications of mathematics.

Mathematics Meets Technology
Looks at the design of mechanisms, for example gears and linkages, through the eyes of a mathematician.

101 Mathematical Projects
As in the preceding collections of puzzles, games and activities, these projects cater to a wide range of concepts and skills and can be linked with other curriculum activities.

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Have more fun on Let’s Play Math! blog:

• The Puzzling Pythagorean Pebbles
• Math Club Nim
• Euclid’s Game on a Hundred Chart
• Hundred Chart Nim
• Tens Concentration