Where has this game been all my life? I’ve always liked dots and boxes for a great on the go waiting or travel game, and the Sim pencil game, also known as “the game of Sim” is a great new discovery for us! It’s more than a game, it’s a brain teaser for two players!
The Sim pencil game was invented in 1969 by Gustavus Simmons, a cryptographer, who described it in the Journal of Recreational Mathematics.
It is a pencil and paper game, so it’s totally free and you can play anywhere with anyone of any skill level. Plus, it’s a great thinking game with a mathematics and geometry twist! Sounds perfect, right?
How to Play the Sim Pencil Game
What you need:
- 2 differently colored pens or pencils
- 2 enthusiastic players
- Your wits
Force your opponent to complete a triangle in his or her color.
How to play:
Play 6 dots on the paper in an hexagonal arrangement as you see in the photo. The dots are the vertices.
Decide who goes first.
The first player (blue) draws a straight line between any two vertices.
The second player (orange) draws a straight line between any two vertices.
Turns alternate in this fashion until one player has completed a triangle in which all three sides are his or her color and thus, loses the game.
In the image grid below you can see the progression. In the final grid you can see the small orange triangle in the upper right, but orange has not lost. The winning triangle must use 3 of the original dots as vertices.
As an alternative to a blank piece of paper, you can pre-draw the possible lines in pencil (see image below, and video demonstration above). Players then trace over lines in their respective color. This is a good alternative for younger kids. Just remember that lines must alway begin and end on the vertices.
About the Sim Pencil Game
If you want some light reading you can read about the mathematics behind a winning strategy for the second player here. It is very difficult to memorize and master the winning strategy, however, so game play is essentially evenly matched between players.
If you are familiar with mathematic theories, you will know that the Ramsey theory applies to Sim game play. I, however, am not equipped to explain Ramsey theory to you. I will leave that to the professionals. Read about Ramsey theory here.
More brain teasers and games!
Pentalpha, a star-shaped brain teaser puzzle
T-puzzle, a puzzle and brain teaser in one!