Avoid Three Game (and Challenge Puzzle)

Avoid Three is an interesting game for two players that is played with a checkerboard and a small number of game pieces such as bingo chips or pawns.

Don’t have someone to play with? Read on to find a mathematical puzzle for you or your students to solve.

Supplies for Avoid Three

Avoid Three can be played on a standard checkerboard or chessboard with any small game pieces of your choosing. I recommend bingo chips, game pawns, or mini erasers. But anything small would work – even coins or small bits of paper.

If you don’t want to present the game to others on physical gameboard, I have created a printable version of the game with instructions for playing printed above the checkered gameboard.

Game Instructions

Avoid Three is a game for two players. Take turns placing a game piece on the checkered board. The first player to form a line containing three game pieces (horizontally, vertically, or diagonally) loses.

Source of Game

I ran across this game in Mathematical Activities: A Resource Book for Teachers by Brian Bolt (Cambridge University Press, 1982). I have several of Brian Bolt’s books by my desk, and I am always inspired whenever I flip through them.

According to Brian Bolt, “The skill in the game is to select patterns of play which force your opponent into having to complete a line.”

In the book, he provides a picture of gameplay that features twelve pieces on the board. So, if you are strategic, you can place quite a few pieces on the board before a line of three is formed.

Alternative Puzzle Version

In Brian Bolt’s write-up of the Avoid Three Game in Mathematical Activities: A Resource Book for Teachers, he shares an interesting fact about the largest number of pieces that can be placed on the chessboard without having any three pieces forming a line vertically, horizontally, or diagonally.

I thought it would be interesting to turn this into a puzzle for students to figure out what this magic number is

So, I took the gameboard and edited it slightly to make the “Avoid Three Challenge.”

Now that I’m writing this blog post, I’m second guessing my wording on this. I think I actually should have clarified that “no horizontal, vertical, or diagonal line contains three or more pieces.”

I envision this being a class challenge where students compete to see who can place the highest number of game pawns on the board without forming a line of three.

What is the largest number of pieces that can be placed on the checkerboard below (one piece per square) so that no horizontal, vertical, or diagonal line contains three pieces?

Creating Seasonal Versions

If you want to turn this into a seasonal activity, I recommend playing the game with seasonal mini erasers such as fall mini erasers, winter mini erasers, or Christmas mini erasers. (You could also print and cut out seasonal shapes for whatever holiday is coming up next.)

I recently bought a few sets of mini erasers from Amazon to use with activities with my five-year-old. I discovered that they are perfect for classroom puzzles and games as well.

My son and I tested this game out over several days with different themed erasers. We even picked the pumpkin erasers out of the fall mini erasers set to make a Halloween themed game on Halloween.

Follow Up to 8 Queens / 8 Bats Puzzle

Speaking of seasonal puzzles, if your students tackled the 8 Bats Puzzle which is a seasonal twist on the classic 8 Queens Puzzle, they might notice a bit of similarity between that puzzle and this puzzle/game.

This game can actually be a fun follow-up to that puzzle.

There is an important difference between the two, though. In the 8 Queens / 8 Bats Puzzle, you had to form lines that had exactly one piece in each line. In this version, you are allowed to have lines of 0, 1, or 2 pieces. You just cannot have three in one line.