# Sprouts

This is a game for two players. All you need is paper and a pencil. The game starts by drawing three dots.

The first player has a turn by joining two of the dots and marking a new dot in the middle of the line. Or the line may start and end on the same dot.

When drawing a line, it cannot cross another line. (This is important to
remember!)

A dot cannot have more than three lines branching to or
from it. For example, in the game below, dots A and B cannot be used
any more because they already have three lines.

The idea is to make it impossible for the other player to draw a line.

So the last person to draw a line is the winner. What are the winning tactics?

Does it matter who goes first?

Why must the game end after a limited
number of moves? How many?

What happens when you start the game
with four or five dots?

To help you work out a winning strategy, you could begin by playing with just two dots at the start.

Why play this game?

Sprouts offers an engaging introduction to networks, encouraging students to experiment and conjecture. The challenges requires them to work systematically, refine ideas, and eventually find a winning strategy.

### Possible approach

Introduce the game to the class by inviting two volunteers to play against each other. Do this a couple of times, giving each the opportunity of going first.

Ask the students to play the game in pairs. Challenge them to find a winning strategy. As they play, circulate around the classroom and ask them what they think is important.

After a suitable length of time bring the whole class together and invite one pair to demonstrate their strategy, explaining their decisions as they go along. Use other ideas to refine the strategy.

Once students are confident about their strategies they could move on to exploring what happens when the game starts with four or five dots.

### Key questions

Does it matter who goes first?

Why must the game end after a limited number of moves? How many?

### Possible support

You can begin by playing with just two dots at the start.

Possible extension