Play the game Connect Three below, and then take a look at the questions that follow.

This is a mathematical version of noughts and crosses that uses differently numbered dice (one with the numbers $1$, $2$, $3$, $-4$, $-5$, $-6$ and the other with the numbers $-1$, $-2$, $-3$, $4$, $5$, $6$). To place your counter, roll the dice and decide whether to add or subtract the numbers.

You can use the interactive version below or print this board to play away from the computer.

Full Screen Version

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Are some squares easier to land on than others?

I can only land on $12$ if I get a $6$ and a $-6$:
$6 - (-6) =12$

but there are many ways of landing on $4$:
$5 - 1 = 4$
$2 - (-2) = 4$
$(-2) - (-6) = 4$
.....

Can you work out the number of different ways of achieving each of the different totals?

Can these results help you work out a strategy for improving your chances of winning the game?