Connect 4
Introduction: I am going to investigate how many different ways you can win with connect 4.
To start with I am going to use grids with a height of 4 and of varying lengths.
From the table above I can see that there is a pattern with the results. The Length goes up by 4 every time, The Height goes up by 1, The Diagonal goes up by 2 and The Total goes up by 7. From this I can form the prediction that for 4 x 7 the Length will be 16, the Height will be 7, the Diagonal will be 8 and the Total will be 31.
From the results I can see that my prediction was correct and I have now decided to work out a rule so that you can work out the total for any length with height 4. I am going to use the difference method to work out the rule.
4 X 4
4 X 5
4 X 6
4 X 7
Length
4
8
2
6
Height
4
5
6
7
Diagonal
2
4
6
8
Total
0
7
24
31
7 7 7
As you can see the difference is 7, using the difference method if the 1st difference is the same you multiply it by the number in the sequence in this case the length (L). After multiplying the length by 7 you work out how much has to be taken away or added (n).
Premature rule: 7L - n
For the 4 x 5: 7x5 = 35, 35-17 = 18
Rule for Connect 4 with Height 4: 7L - 18
Test Rule:
If the Length is 8: 7x8 - 18 = 38. I predict that the total number of connect 4 for the 4 x 8 grid will be 38.
From this I can see that my rule is correct.
I have now decided to extend the Coursework by trying to work out an overall rule for Connect 4's. For this I'm going to have to work out the connect 4's with heights 5 and 6.
To start with I am going to work out the amount of connects there are for Height of 5 and of varying lengths.
I have decided to tabulate these results so that I can form an overall rule for any length grid with height 5.
5 x 4
5 x 5
5 x 6
Length
5
0
5
Height
8
0
2
Diagonal
Introduction: I am going to investigate how many different ways you can win with connect 4.
To start with I am going to use grids with a height of 4 and of varying lengths.
From the table above I can see that there is a pattern with the results. The Length goes up by 4 every time, The Height goes up by 1, The Diagonal goes up by 2 and The Total goes up by 7. From this I can form the prediction that for 4 x 7 the Length will be 16, the Height will be 7, the Diagonal will be 8 and the Total will be 31.
From the results I can see that my prediction was correct and I have now decided to work out a rule so that you can work out the total for any length with height 4. I am going to use the difference method to work out the rule.
4 X 4
4 X 5
4 X 6
4 X 7
Length
4
8
2
6
Height
4
5
6
7
Diagonal
2
4
6
8
Total
0
7
24
31
7 7 7
As you can see the difference is 7, using the difference method if the 1st difference is the same you multiply it by the number in the sequence in this case the length (L). After multiplying the length by 7 you work out how much has to be taken away or added (n).
Premature rule: 7L - n
For the 4 x 5: 7x5 = 35, 35-17 = 18
Rule for Connect 4 with Height 4: 7L - 18
Test Rule:
If the Length is 8: 7x8 - 18 = 38. I predict that the total number of connect 4 for the 4 x 8 grid will be 38.
From this I can see that my rule is correct.
I have now decided to extend the Coursework by trying to work out an overall rule for Connect 4's. For this I'm going to have to work out the connect 4's with heights 5 and 6.
To start with I am going to work out the amount of connects there are for Height of 5 and of varying lengths.
I have decided to tabulate these results so that I can form an overall rule for any length grid with height 5.
5 x 4
5 x 5
5 x 6
Length
5
0
5
Height
8
0
2
Diagonal
