Tn = 5n-56
19*5=95
-56
39
Here is another 8*8 grid I will use the similar method just like the one on the first page and see what I gate for this second one. The difference between these is that the numbers this time are all different.
T-number = 43
T-total = 26+27+28+35+43=159
T19 = 159
T-number = n
T-total = n+n-8+n-15+n-16+n-17
Tn = 5n-56
T-number = 43
Tn = 5n-56
43*5=215
-56
159
Here is another 8*8 grid I will use the similar method just like the one on the first page and see what I gate for this second one. The difference between these is that the numbers this time are all different.
T-number = 18
T-total = 1+2+3+10+18=34
T19 = 34
T-number = n
T-total = n+n-8+n-15+n-16+n-17
Tn = 5n-56
T-number = 18
Tn = 5n-56
18*5= 90
-56
34
As you have seen from the above diagram and from the diagram on the first page as well the second page, the Tn answer is the same, Tn = 5n-63, so my prediction on this was correct and in this case it also makes it clear that all the other 8*8 grids will produce the same answers.
I’m now going to investigate a 7*7grid, my aim is similar to those of 8*8 and 9*9 grids, to find out whether it is similar to those or not.
T-number = 16
T- total = 1+2+3+9+16=31
T16 =31
T-number = n
T-total = n+n-7+n-13+n-14+n-15
Tn = 5n-49
T-number = 16
Tn = 5n-49
16*5=80
-49
31
Here is another 7*7 grid I will use the similar method just like the one on the first page and see what I gate for this second one. The difference between these is that the numbers this time are all different.
T-number = 17
T- total = 2+3+4+10+17=36
T16 =36
T-number = n
T-total = n+n-7+n-13+n-14+n-15
Tn = 5n-49
T-number = 17
Tn = 5n-49
17*5=85
-49
36
As you have seen from the above diagram and from the diagram on the first page the Tn answer is the same, Tn = 5n-49 so my prediction on the third diagram is that after all Tn algebra will still remain the same.
Here is another 7*7 grid I will use the similar method just like the one on the first page and second page. There is no difference between them apart fro the T-numbers in the T-shape.
T-number = 20
T- total = 5+6+7+13+20=51
T16 =51
T-number = n
T-total = n+n-7+n-13+n-14+n-15
Tn = 5n-49
T-number = 20
Tn = 5n-49
20*5=100
-49
51
As you have seen from the above diagram and from the diagram on the first page as well the second page, the Tn answer is the same, Tn = 5n-49, this perfectly makes my prediction correct and it also proves that all the 7*7 grids will have the same answers no matter what the numbers.
I’m now going to investigate the 6*6 grids.
T-number = 14
T-total = 1+2+3+8+14=28
Tn = 28
T-number = n
T-total = n+n-6+n-11+n-12+n-13
Tn = 5n-42
T-number = 14
Tn = 5n-42
14*5=70
-42
28
Here is another 6*6 grid I will use the similar method just like the one on the first page and see what I gate for this second one. The difference between these is that the numbers this time are all different.
T-number = 15
T-total = 2+3+4+9+15=33
Tn = 33
T-number = n
T-total = n+n-6+n-11+n-12+n-13
Tn = 5n-42
T-number = 15
Tn = 5n-42
15*5=75
-42
33
As you have seen from the above diagram and from the diagram on the first page the Tn answer is the same, Tn = 5n-42 so my prediction on the third diagram is that I think the Tn algebra will still remain the same.
Here is another 6*6 grid I will use the similar method just like the one on the first page and second page. There is no difference between them apart from the T-numbers in the T-shape.
T-number = 29
T-total = 16+17+18+23+29=103
Tn =103
T-number = n
T-total = n+n-6+n-11+n-12+n-13
Tn = 5n-42
T-number = 29
Tn = 5n-42
29*5=145
-42
103
As you have seen from the above diagram and from the diagram on the first page as well the second page, the Tn answer is the same, Tn = 5n-42, this perfectly makes my prediction correct and it also proves that all the 6*6 grids will have the same answers no matter what the numbers.
I’m now going to investigate the 5*5 grid and see how different it is compared to 9*9, 8*8, 7*7 and 6*6.
T-number = 12
T-total = 1+2+3+7+12=25
Tn = 25
T-number = n
T-total = n+n-5+n-9+n-10+n-11
Tn = 5n-35
T-number = 12
Tn = 5n-35
12*5=60
-35
25
Here is another 5*5 grid I will use the similar method just like the one on the first page and see what I gate for this second one. The difference between these is that the numbers this time are all different.
T-number = 18
T-total = 7+8+9+13+18=55
Tn = 55
T-number = n
T-total = n+n-5+n-9+n-10+n-11
Tn = 5n-35
T-number = 18
Tn = 5n-35
18*5=90
-35
55
As you have seen from the above diagram and from the diagram on the first page the Tn answer is the same, Tn = 5n-35 so my prediction on the third diagram is that I think the Tn algebra will still remain the same.
Here is another 5*5 grid I will use the similar method just like the one on the first page and second page. There is no difference between them apart from the T-numbers in the T-shape.
T-number = 23
T-total = 12+13+14+18+23=80
Tn = 80
T-number = n
T-total = n+n-5+n-9+n-10+n-11
Tn = 5n-35
T-number = 23
Tn = 5n-35
23*5=115
-35
80
As you have seen from the above diagram and from the diagram on the first page as well the second page, the Tn answer is the same, Tn = 5n-35, this perfectly makes my prediction correct and it also proves that all the 5*5 grids will have the same answers no matter what the numbers.
The final investigation is on a 4*4 grid, this would prove that the formula I’m using can work on any grid.
T-number = 10
T-total = 1+2+3+6+10=22
Tn = 22
T-number = n
T-total = n+n-4+n-7+n-8+n-9
Tn = 5n-28
T-number = 10
Tn = 5n-28
10*5=50
-28
22
Here is another 4*4 grid I will use the similar method just like the one on the first page and see what I gate for this second one. The difference between these is that the numbers this time are all different.
T-number = 14
T-total = 5+6+7+10+14=42
Tn = 42
T-number = n
T-total = n+n-4+n-7+n-8+n-9
Tn = 5n-28
T-number = 14
Tn = 5n-28
14*5=70
-28
42
As you have seen from the above diagram and from the diagram on the first page the Tn answer is the same, Tn = 5n-28 so my prediction on the third diagram is that I think the Tn algebra will still remain the same.
Here is another 4*4 grid I will use the similar method just like the one on the first page and second page. There is no difference between them apart from the T-numbers in the T-shape.
T-number = 15
T-total = 6+7+8+11+15=47
Tn = 47
T-number = n
T-total = n+n-4+n-7+n-8+n-9
Tn = 5n-28
T-number = 115
Tn = 5n-28
15*5=75
-28
47
As you have seen from the above diagram and from the diagram on the first page as well the second page, the Tn answer is the same, Tn = 5n-28, this perfectly makes my prediction correct and it also proves that all the 4*4 grids will have the same answers no matter what the numbers.
