# Traffic Lights

I invented Traffic Lights because I wanted a five-minute game with the accessibility of Noughts and Crosses but also enough depth to make players think a bit. And whereas Noughts and Crosses is frankly a bit boring once players have discovered the thing to do is grab the central square and then with sensible play you must get at least a draw, in Traffic Lights draws are impossible and someone has to win.

Here are the rules:

1……The game is played on a 3×3 board of squares. At the start of the game all the squares are empty.

2……When it is your turn to play you have three options:

• (a) you may place a red counter into any empty square, or
• (b) you may replace an existing red counter with an orange counter, or
• (c) you may replace an existing orange counter with a green counter.

3……You win if you place the final counter that completes a row / column / diagonal of three pieces of the same colour. (Whoever played the previous counters in the row is immaterial; it is the third counter that wins the game.)

Here’s the start of a game.  I play first:

And I play a further red:

Your turn.  Time to introduce an orange (by the way, I found my orange counters came out looking very reddy, so I’m using yellow ones).

There’s a nice sense of momentum in the game.  The board begins to fill and the number of possible choices decreases, while the number that lead to instant disaster rises.  After a few turns we’ve reached this stage, and there only seven possibilities, of which – I think – four lose immediately:

For example, promoting the red at the bottom left gives:

And this allows the promotion of the last red, creating a winning orange line:

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Traffic Lights has always been just about the most popular of my games.  I think it probably first appeared on NRICH at  http://nrich.maths.org/1181 .  It’s been played by six and seven yearolds as well as adults, and has often been used in competitions for primary pupils in Portugal.

Once you’re used to the basic version, you ought to play on a 3×4 board.

There are some more references at  http://www.di.fc.ul.pt/~jpn/cnjm8/

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