### Consecutive Numbers

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

### Pair Sums

Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?

### Negative Dice

If the odd numbers on two dice are made negative, which of the totals cannot be achieved?

# Playing Connect Three

##### Age 11 to 14 Challenge Level:

Below are two games in which the winner is the first to complete a row of three, either horizontally, vertically or diagonally.

In the first game, you roll the dice, place each dice in one of the grey squares, and decide whether you want to add or subtract them, to produce a total shown on the board. Your total will then be covered with a counter.

You cannot cover a number which has already been covered.
If you are unable to find a total which has not been covered you must Pass.

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

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Which numbers belong to most winning lines?
Does this influence the way in which you might choose to play the game?

The second game is played with two special dice, one with the numbers $1, 2, 3, -4, -5, -6$ and the other with the numbers $-1, -2, -3, 4, 5, 6$.
Choose what order to place the dice in, and add or subtract them to produce one of the totals shown on the board, which you can then cover with one of your counters.

Play the game a few times, and then take a look at the questions below.
You can use the interactive version below or print this board to play away from the computer.

If you can see this message Flash may not be working in your browser
Please see http://nrich.maths.org/techhelp/#flash to enable it.

Some numbers can only be made in one way, but some can be made in many different ways.

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

Does this influence the way in which you might choose to play the game?