D Box
The first value will always be two, the second value will be the squared number from the first value in the horizontal/vertical box
The algebra term
H+V+D = total amount of winning lines
Rectangle grids for connect four on next page.
Rectangle grids on connect four
4x5
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
Connect 4 rectangle grid
Connect 3 square grids
I’m now going to use my results to predict connect 3 grids for rectangle grids
So now you should be able to predict a 6x7 grid with the connect 4 rule.
Evaluation
I think that the whole of the investigation went well overall, I started by a 4x4 grid with the connect 4 rule, followed by a 5x5 grid. I then looked for a pattern in the to grids to predict what the winning lines would be for a 6x6. After predicting I tested the theory out by drawing a 6x6 grid and a table to compare my results against my prediction. My prediction was right, so I moved on to make a formula for connect 4 square grids. I figured out that I should write it out in an algebra formula. After completing the formula I tried it out. It worked, so that I knew that I had completed connect 4 square grids.
I moved onto connect 4 rule on rectangles, starting off with a 4x5 grid. After doing this with a 4x6 grid I tried to find a pattern again. When I thought that I had found a pattern I decided to test it out. Once again the prediction matched the total winning lines. I then looked for a formula that would show how to calculate a connect 4 rule on a rectangle grid. After I had a formula that I thought would work, I tested it and the result was the same as last time. It worked.
After doing connect 4 rule on squares and rectangle grids I thought that I would try connect 3 rule. So I started with a 3x3 grid, because that is the smallest amount you can have for a connect 3 grid. I wrote down the results in a table as previously, after doing a 3x3 grid I moved onto a 4x4 grid with the connect 3 rule. When writing down the 4x4 grid, I thought that I had found a pattern, but I was wrong, so I did a 5x5 grid. After putting that into a table, I found the pattern for a connect 3 squared grid . It was pretty similar to a connect 4 rule with squared numbers in. I then tested my formula for connect 3 squared grids, and I was right.
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.
