## A game of Sprouts

By David, 10 February 2015 Activity

Draw a few dots on a page.

Sprout some cute little plant networks in this mathematical drawing game.

### You will need

- Pencil and paper
- Someone to play with

### What to do

- Draw at least two big dots on the paper. These are called spots.
- Decide who gets to go first.
- On your turn, draw a line from one spot to another spot.
Draw a line between two dots and draw a new dot on the line.

- When you finish drawing your line, put a spot somewhere along its length, splitting the line in two.
- There are two rules you need to follow:

- A line can’t cross over itself or other lines.
- A spot can only have three lines coming out of it.

- Once you finish your turn, it is your opponent’s turn. Keep alternating turns until it is impossible to draw a line. Whoever played the last move wins!
The right dot has three lines and cannot have any more coming from it.

### What’s happening?

When you first read the rules of Sprouts, you might think it never ends – you’re always adding new spots to connect. But spots can be filled up, which gives us a hint why the game always ends.

Each spot can only have three lines coming out of it. You can imagine that each spot has three lives. On your turn, you draw a line that goes to two existing spots, using up one life for each. You also add a spot, but it already has two lines connecting it, so it only has one life left. You use up two lives and only add one. Eventually these lives will run out and you won’t be able to add more lines.

You can make the game end faster by separating the spots that are still alive. If a spot is encircled by lines, it can’t connect to a spot outside the circle – so the game can end while there are still several lives left. If you play with three spots at the start, the first player has to do this to win.

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