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Choose any three by three square of dates on a calendar page. Circle any number on the top row, put a line through the other numbers that are in the same row and column as your circled number. Repeat this for a number of your choice from the second row. You should now have just one number left on the bottom row, circle it. Find the total for the three numbers circled. Compare this total with the number in the centre of the square. What do you find? Can you explain why this happens?

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Domino Square

Use the 'double-3 down' dominoes to make a square so that each side has eight dots.

Playing Connect Three

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

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

This text is usually replaced by the Flash movie.

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?