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As part of my G.C.S.E Maths we had to do a piece of coursework on connect four winning lines.

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Introduction

Maths Coursework

As part of my G.C.S.E Maths we had to do a piece of coursework on connect four winning lines. I’m going to start my investigation with a 4x4 because it is the smallest possible winning line in a connect 4 game. I will then move onto a 5x5 grid, hopefully after that I could predict a 6x6. After completing square grids I will move onto rectangles. The data I will need to know is the area of a full size connect four grid (6x7) and that you can only go in a straight line of a 4 counter horizontally, vertically and diagonally.image04.jpg

image00.png

I think that I have found a pattern, which will enable me to predict a 6x6 grid to find the winning line

Grid size

h

v

d

Total

6x6

3x6

3x6

2x9

54

Grid size

h

v

d

total

4x4

1x4

1x4

2x1

10

5x5

2x5

2x5

2x4

18

6x6

3x6

3x6

2x9

54

As you can see the h,v,d all have a pattern

H Box

           The horizontal box has a pattern of plus three values from the first value to the second value.

V Box

           The Vertical box on the grid has the same pattern as the h box.

...read more.

Middle

4x6

4x7

image02.png

I’m now going to try adding a new rule into connect 4.It will be connect 3, this will be on the next page.

Connect 3 square grids

As this is connect 3, the smallest grid size you can have is 3x3. This is what grid size I’m going to start with, then I will move onto 4x4, 5x5.

3x3

5x5

4x4

image03.png

I will now compare all my results together.

Comparison of Results

Connect 4 square grids

Grid size

h

v

d

total

4x4

1x4

...read more.

Conclusion

I moved onto connect 3 rule on rectangles, starting off with a 3x4 grid. After doing this with a 3x5 grid I tried to find a pattern. When I thought that I had found a pattern I decided to predict the next grid a 3x6. Once again the prediction matched the total winning lines. I then looked for a formula to try and show any size of rectangle with a connect 3 rule on a rectangular grid. After I had a formula that I thought would work, I tested it out and the predictions were correct.

If I could change anything that I did in my investigation it would be to go back and change both values in the grid size’s of the rectangles because then I could have a wider prediction on rectangles. Another thing that I would have liked to change would have been to have more testing and predicting.  

...read more.

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