The game uses a 3x3 square board. 2 players take turns to play,
either placing a red on an empty square, or changing a red to
orange, or orange to green. The player who forms 3 of 1 colour in a
This game for two players comes from Ghana. However, stones that were marked for this game in the third century AD have been found near Hadrian's Wall in Northern England.
Reasoning based on this Japanese activity.
This is a game for two players.
Start by drawing a number line from $0$ to $20$ like this:
You can find some of these number lines here.
The first player chooses a number on the line and crosses it out.
The same player then chooses a second number and crosses that out too.
Finally, he or she circles the sum or difference of the two numbers and writes down the calculation.
For example, the first player's go could look like this:
The second player must start by crossing off the number that player $1$ has just circled.
He or she then chooses another number to cross out and then circles a third number which is the sum or difference of the two crossed-off numbers.
Player $2$ also writes down their calculation.
For example, once the second player has had a turn, the game could look like this:
Play continues in this way with each player starting with the number that has just been circled.
For example, player one could then have a turn which left the game looking like this:
The winner of the game is the player who stops their opponent from being able to go.
This powerpoint presentation also demonstrates how to play the game. You may like to click through it.
Now it's your turn!
Try playing the game a few times to get a feel for it.
What is your strategy for winning?
Click here for a poster of this problem.