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Consecutive Numbers

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

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Pair Sums

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

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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:

Daniel from Gateway Primary School, noted that:

It is hardest to get $12$ and negative $12$. You are most likely to get the low positive and negative numbers. You are least likely to get the high positive and negative numbers.

Jeremy from Longston School wrote:

I wrote a table of all the numbers you can get, and then looked at how many ways of making each number there are:

Then you can see that getting a $3$ or $-3$ are most likely to happen. So you should place a counter near the $3$ or $-3$ because then you are most likely to get it next turn, and then you will have two in a row.

Aidan commented:

You should always aim to get $0$, as is it is in the centre of the grid, and offers the most possibilities. And if the other person has two in a row, you should block them like noughts and crosses if you can.

Very well noticed by everyone. Can anyone add further comments?