This is a game for two players.

You need the game board shown below. It is easy to draw if you want to play this on paper. You will need two different colour pencils (highlighters are good to use).

The dots are towns. The 9 straight lines are roads going to and through the towns.

Each player takes a turn to colour over a whole straight road (even though it may pass through several towns).
The first player to colour three roads going to or through the same town wins.

Eight nodes joined together with nine lines. Each node has 3 lines leading to or passing through it.
Does it matter which player goes first?
Which road is it best to colour first?

What happens to the game if you add another road or two?

Can you analyse the elements and structure in the following games and the correspondences between them?  Describe the patterns that show they are equivalent games that can be played using equivalent strategies.

We suggest tackling them in the order given.

Ages 14 – 16

Math Topics
Deductive Reasoning & Logical Thinking
Middle School, High School
9th Grade, 10th Grade, 11th Grade

What are you looking for?


NRICH (University of Cambridge)

Website URL

Type of Resource

Board/Card Game

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