Problem Teachers' Notes Hint Solution

# Playing Connect Three

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?