Middle School

The Take-Away Game

A recent visit to a 6th-grade classroom gave me a chance to introduce a simple game I have used in the past as an-going challenge.  Even after a few pop-ins to this 6th grade class, I am still undefeated, and don’t plan on giving up my championship belt anytime soon!


On a board, or piece of paper, draw 23 X’s.  Players will alternate turns, and on each turn a player must erase 1, 2 or 3 X’s.  The winner is the player who erases the last X.

It’s an easy game to understand.  An example is given here:

With a class, I will give students a chance to use dry-erase boards and play against each other.  Then, as students begin to understand the game, they are allowed to challenge me.  This usually ends badly (for them), as I know the tricks to the game.  I start by asking the player if they would like to go first, or allow me to go first.  Since kids are usually nice, they will allow me to go first, and this sets them up for certain doom.  Also, I will use my best poker skills to agonize over my moves, though I know exactly where I want to go with my moves.

Eventually, students will gather around to suggest moves.  Their first realization is that if I get the board down to 4 Xs, I will win.  This will then extend to 8 remaining.  With some classes, I have placed a fist behind my back, and done a thumbs-up to signal those watching when I know I have the game won.  Shoot me an e-mail if you need thorough instructions on how to win.

As students master the game, we can ask some extension questions:

  • Does the number of X’s we draw change the game?  What if we use 25, 35, or 50 X’s?
  • What if we could erase 4, 5, 6 or n number of X’s?  How would the strategy change?

For now, play the game with your students, and I look forward to retaining my Inter-Galactic Take-Away Game BeltChampionship Belt!


By Bob Lochel

HS Math Teacher. Hatboro-Horsham School District, Horsham, PA.

3 replies on “The Take-Away Game”

I call this game Nim 21 (because we start a typical game with 21 stones). Lot’s of great extensions and variations. You might even be surprised to find that your students create the more traditional game of Nim themselves. Here are a few examples some of my students have come up with:
*You can take away 2, 3, or 4. If you end up with 1 left over, it’s a tie
*Roll a die each turn to see how many stones you can remove
*Play with 3 players
*You can take away any Fibonacci #.

Leave a Reply

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s