In our last article, we focused on Africa, the birthplace of mathematics for simple math games involving counting and strategy. We are now going to venture outside of this rich continent of math history and travel to Asia and Europe.
One of the most popular and everlasting games that has been around for a long time is Nim. Scholars believe the game can be traced back to China, but there is still no concrete proof of this.
The game of Nim is a two player math game. Each player takes turns removing objects from the piles or heaps in front of them. When it is your turn, you must remove at least one object. However, you are allowed to remove more than one object from a single pile or heap. To win, you must be the person who takes the last remaining object.
The game is simple to play but it takes quite a while to figure out the strategy. As illustrated in the picture above with the accompanying rules, Nim is a take-away game where the piles of stones/counters can vary — it doesn’t have to form a pyramid or any set structure. You could, for example, have 3 stones in the first row, 7 in the second, 5 in the third, 17 in the fourth, etc.
The key strategic insight is that you need to pick one row and then remove as many stones as you want from that row. The mathematics for this optimum strategy will lead to students learning about binary numbers!
Sim (North America)
When you hear the name of this game, you might think there is a relationship to the game “Nim” in some fashion. In fact, the games are completely different in every conceivable way, except that there is an optimal strategy to winning — a characteristic of many great math games!
Sim is a two-player pencil and paper game that was created 50 years ago by the cryptographer Gustavus Simmons.
The easiest way to play the game is to draw six dots in the form of a hexagon and lightly draw in lines with a pencil connecting all six dots.
Players take turns tracing over these lines with their respective colors. What each player is trying to do is avoid making a triangle with all the sides of that color. It kind of has a “tic-tac-toe” feel. Again, this is a really fun game, but has a lot of deep mathematics embedded below the surface!
Mu Torere (New Zealand)
This game was created by the Maori people in New Zealand. As a game created by indigenous people, the elements of simplicity and accessibility are key traits. Meaning that, while the game is often played on elaborate boards, it can also be played in the sand!
Here is a link to a fun video that quickly explains the game!
Like many games we have discussed, Mu Torere involves the specific movement of player pieces on the game board until there is a point at which no legal moves can be made by one player.
Ideas like mathematical reasoning, proof, and graph/network theory are inextricably woven into the tactics of the game.
Seega is a late 19th-century game from Egypt. It is a capture game that utilizes only perpendicular movements of the game pieces. It is played on a 5 x 5 board with.
- Take turns placing two stones at a time on any two vacant squares, except for the central square which is left empty to begin with.
- When all 24 stones have been placed, the player placing the last couple in position begins the second stage.
- A stone can move at right angles (but not diagonally) into any adjacent empty square including the centre square.
A stone is captured and removed from the board when an enemy stone is moved alongside, trapping it by two enemy stones, one on each side. In the diagram, when the red stone is moved as shown, it captures all three blue stones simultaneously.
- After making a capture, a player can continue to move the same stone as long as it makes further captures.
- Safe ground: a player can safely move a stone between two enemy stones. Also, a stone on the central square cannot be captured.
- When a player cannot move, the opponent must make an entry by taking an extra turn.
The winner: a player wins outright if he can capture all the enemy stones.
There are literally hundreds of math games from around the world that employ not only various kinds of mathematical thinking, but because of their humble origins, they can usually be played with everyday household objects.
Hope you have fun playing these games with your students!