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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.

avoid three game with pawns on both sides of chessboard.

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.

avoid three game with pile of bingo chips.

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.

avoid three game board for two players

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.”

avoid three game with bingo chips on board.

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.”

instructions and game board for avoid three challenge on chessboard.

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?

avoid three challenge puzzle with pawns on board.

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.)

fall and christmas mini erasers in plastic containers.
avoid three challenge with winter or christmas mini erasers.

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.

avoid three game with pumpkin mini erasers.
avoid three game with christmas mini erasers.

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.

Puzzle Solutions

I intentionally do not make answers to the printable math puzzles I share on my blog available online because I strive to provide learning experiences for my students that are non-google-able. I would like other teachers to be able to use these puzzles in their classrooms as well without the solutions being easily found on the Internet.

However, I do recognize that us teachers are busy people and sometimes need to quickly reference an answer key to see if a student has solved a puzzle correctly or to see if they have interpreted the instructions properly.

If you are a teacher who is using these puzzles in your classroom, please send me an email at sarah@mathequalslove.net with information about what you teach and where you teach. I will be happy to forward an answer key to you.

Not a teacher? Go ahead and send me an email as well. Just let me know what you are using the puzzles for. I am continually in awe of how many people are using these puzzles with scouting groups, with senior adults battling dementia, as fun activities in their workplace, or as a birthday party escape room.

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