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# Sprouts - A Two Player Game

Lesson Plans > Mathematics > Problem Solving > Strategy Games

## Sprouts - A Two Player Game

When I was in high school, a friend taught me a pencil and paper game that he called 'Sprouts'. Since then I have taught the game to both children, teens, and adults. Reactions to the game vary depending on the personality of the player; some treat it as a game of luck (which it is not) and will play it again and again with the same abandon as they might play the card game 'War'.

Others are quick to analyze the strategic possibilities of the game.

The object of the game is to be the last person who can draw a line on the paper, following the rules outlined below.

Setting up the game
The students agree before the game begins how many dots to place on the paper. This may be a number anywhere from five on up - but keep in mind that the length of the game increases with the number of dots on the paper.

Dots should be drawn large enough that they are still visible when lines are drawn through them. Students can take turns adding dots to the page, or one student can be designated to create the 'playing field'

Playing the game
Players do the following each time it is their turn:

1. Draw a line (can be curved) connecting any two dots on the page, making sure the line does not cross any other lines. NOTE: a 'circular' line can be drawn connecting a dot to itself.

2. Add a new dot (the 'sprout') somewhere on the new line.

3. If either of the dots on the ends of the line have three lines connecting it, draw an 'X' through the dot, so it can't be used any more.

4. A dot can also be 'X-ed' if both players agree that it is 'cut off' from the rest of the dots, and cannot have any more lines drawn to it.

The winner is the person who draws the last line, leaving the opponent unable to add any more lines using the rules above. The following series of images shows the first few moves in a game of Sprouts.

Setting up the game:

First turn:

Second turn:

Third turn:

Fourth turn:

After playing a few games, it will become evident that the number of dots, as well as who goes first, plays a significant role in who wins. However, closer analysis reveals that there are strategies which will give an advantage to the player who knows them. Figuring out the strategy involved is great problem solving practice and prepares students to begin learning some fundamental concepts in topology.

This little activity is a great addition to any teacher's arsenal of rainy day classroom activities.

Lesson by Mr. Twitchell