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Game of Sim

The game of sim is an easy-to-learn pencil and paper game of drawing lines and avoiding triangles. Unlike many other similar pencil and paper games, there is always a winner!

I used this as a filler activity on the first day of school after we participated in a collection of number contests. It went super well, and students were still talking about the game where they made triangles for days after!

Rules for Playing the Game of Sim

The Game of Sim is a game for two players. It is played on a template that has six points arranged in the shape of a regular hexagon.

game of sim template

Each player should have their own color to draw their lines in.

Using different colors, players take turns drawing lines to connect any two of the vertices on the diagram. Each line can only be used one time.

Players continue taking turns until a player forms a triangle that is solely made up of their color. The first player to form a triangle in their color LOSES.

The game’s creator, Gustavus J. Simmons, specifies that “only those [triangles] with vertices on the six starting points” count. If you happen to create a small triangle caused by intersecting lines, this is fine. It does not end the game.

For example in the game below, the red player would not lose because though a red triangle is formed, it only has two of the original vertices as corners instead of all three vertices.

example of non-triangle in game of sim

Using the Game of Sim in the Classroom

To speed up game setup and game play, I created a free printable Sim template which is meant to be printed and used inside a dry erase pocket.


dry erase pockets

I cannot imagine teaching math without my dry erase pockets! They instantly make any activity more engaging and save me countless hours at the copy machine since I can use the same class sets of copies year after year.

Here are my current go-to recommendations:

hand holding up template for game of sim in dry erase pocket in high school math classroom

Each pair of students used a different color of expo dry erase marker.

pile of dry erase pockets full of templates for the game of sim

I pre-connected all of the vertices with dashed lines on the dry erase template so students could easily see all of their possible moves with just a glance.

game of sim in dry erase pocket in high school math classroom

Game play is relatively quick, but I can guarantee you that students will want to keep playing game after game as they try to come up with a winning strategy to reliably beat their teammate.

game of sim being played in dry erase pocket

History of the Game

The game of Sim was created by Gustavus Simmons. Simmons named the game after himself and introduced the world to the game in 1969 through an article in the Journal of Recreational Mathematics.

Simmons suggested in his journal article that the game was superior to nim since the game is not trivial and tic-tac-toe since it is impossible to tie this game.

Simmons commented, “In view of its non-trivial nature and tricky strategy, I’m surprised that this game has not replaced TIC-TAC-TOE as a time waster among students.”

student playing game of sim in dry erase pocket