# 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.

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.

Middle

4x6

4x7

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

I will now compare all my results together.

Comparison of Results

### Connect 4 square grids

Grid size | h | v | d | total |

4x4 | 1x4 |

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.

This student written piece of work is one of many that can be found in our GCSE Number Stairs, Grids and Sequences section.

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