Make Your Own Nim Games

Nim is a pure strategy game for two players. On each turn, players remove an option until finally no choice remains.

Game options might include:

• How many stones to take from a pile.
• Which position to claim on a gameboard.
• How far to count in a given sequence.

The rules can vary at the players’ whim (as long as both players agree). How many possibilities do you start with, what are the rules for removing options, and how do you win or lose the game? Everything is open to change. And with every tweak, players must reanalyze their strategy.

The History of Nim

For centuries, people all around the world have played Nim-like folk games, though the rules are rarely written down. Some say Nim originated in China because the rules are similar to the Chinese game Jian-shízi, or “picking stones.”

The first version of the game in print dates to about 1500 in a book of mathematical recreations by Luca Pacioli, a Franciscan friar who also collaborated with Leonardo da Vinci on a geometry book.

Charles Bouton coined the modern name (perhaps based on the German word for “to take”) and brought mathematical attention to the game with his 1901 article “Nim, A Game with a Complete Mathematical Theory.” But it was Martin Gardner who made the game famous when he wrote about Nim in his Scientific American column “Mathematical Games” in 1958.

How Is This Math?

Mathematicians enjoy studying patterns, whether they are patterns within our system of numbers or patterns of shapes or of abstract ideas.

Did you know there’s a branch of mathematics called game theory? Game theorists study patterns of logical decision-making.

They began by studying the pattern of wins and losses in 2-player strategy games like Nim. Now the science has grown into a study of much larger and more complex “games” like politics and economics.

First, Play Several Nim Games

When we reason about game strategy, that’s mathematical thinking. We are dealing logically with the things we see and the facts we know.

So try one of the Nim games on my blog:

• Math Club Nim
• Hundred Chart Nim

Or play some of the sample games (some with printable gameboards) in my activity guide Creative Nim: Make Your Own Math & Logic Games.

And then take a break and talk about the things you noticed. Wonder together about what might happen the next time you play.

• Did you figure out a winning strategy?
• How might your opponent try to block you?
• Would you rather play first or second, or does it matter?

Then, Make Your Own Math

When you create your own games, you do mathematical reasoning at a deeper level, considering the types of choices to give your players and how limiting those options will affect the game.

First, think about a theme or story behind your game. Perhaps your players are dragons trying to hide their gold, or ninja warriors trying to sneak into an enemy camp, or birds building nests on the branches of a tree. Or would you rather make an abstract game of counting or picking up stones?

Will you stick to the tradition of a 2-player strategy game, or will you make a way for more people to join in the fun?

Decide what options players will have in your game:

• Will they be taking physical items like stones or game pieces?
• Will they be moving or claiming positions on a gameboard?
• Or will they be choosing among abstract ideas like numbers or shapes?

In a Nim game, players remove options on each turn until no choices remain. How will players remove options in your game? What choices can they make? What are the limits? How will they win (or lose) the game?

Write out the instructions for your game. Copy what you need from the games in this book, modifying the rules to fit the way you want to play. Draw your gameboard, if needed, and collect whatever game pieces you desire.

Test your new game by playing with a friend. How did it go? Do you want to tweak the rules?

A Puzzle for You

Think about all the games you know. How many can you find that have the features of a Nim game?

Buy the Printable Guide

Did you know there’s a branch of mathematics called game theory? Game theorists study patterns of logical decision-making.

Mathematicians began by studying the pattern of wins and losses in 2-player strategy games like Nim. Now the science has grown into a study of much larger and more complex “games” like politics and economics.

Encourage your children to enter the fascinating world of game theory by creating their own Nim-style math and logic games.

Creative Nim includes instructions and teaching tips, several sample games, and make-your-own-game worksheets in full color and ink-saving black-and-white.

For ages 8 and up.

FORMAT: 47-page printable PDF file with your choice of 8.5″×11″ (letter size) or A4 pages.

GET IT TODAY

And start making math with your kids!