13 + 14 + 15 + 24 + 34 = 100
14 + 15 + 16 + 25 + 35 = 105
T-Total and T-Number grid
I have done 4 T’s so that I can be sure of the pattern I come across.
The pattern I have come across is that every T-number goes up by 1, the T-total seems to go up 5. The rule I believe could be:
T Total = 5N +?
N is the T Number.
I will have to do two more grids to see if I am right but I am pretty certain of what I have done. The next grid I will be doing is the 9 x 9 grid.
4 + 5 + 6 + 14 + 23 = 52
5 + 6 + 7 + 15 + 24 = 57
6 + 7 + 8 + 16 + 25 = 62
7 + 8 + 9 + 17 + 26 = 67
T-Total and T-Number grid
I have come across the same formula in this grid that I did before of:
T Total = 5N +?
N is the T Number.
This is a formula which I believe is the true pattern but I needed to do the 8 x 8 gird to be sure. I also think that I have come across a new formula which can only be proven if the next formula goes down 7 in its T total. The last two have been:
5t -70 = 10 x 10 grid
5t -63= 9 x 9 grid
If it goes down another 7, which I believe it will, that will give me another formula to go off. I will now continue onto the 8 x 8 grid.
25 + 26 + 27 + 34 + 42 = 154
26 + 27 + 28 + 34 + 43 = 159
27 + 28 + 29 + 35 + 44 = 164
28 + 29 + 30 + 36 + 45 = 169
T-Total and T-Number grid
In the 10 x 10 grid, the formula of the T-Total went:
For the 9 x 9, The Algebraic Values were:
And for the 8 x 8 grid the Algebra was:
There appears to be a link in each formula since 70, 63 and 56 are all multiple of 7.
There is also a link how with the size of the grid.
G is the size of the Grid
Summary
Using the formula 5N – 7G, I think I can predict the T total for any T Number in any sized grid, I would predict that in a 7 x 7 grid:
Where N is 16 then the T Total will be equal to 5N-7G =5 x 16 – 7 x 7
=80 – 49
=31
Also this can be worked out by adding the number 1+2+3+9+16=31. As I demonstrated this works.
Conclusion
From the very first grid, I found the right sum but everything that is found out still needs to be checked unless 100% right. I had made a prediction and I turned that into an answer after looking at two more grids. After completing the three grids (10x10, 9x9 and 8x8), I found that every time that the T-Number goes up 1, the T-Total will go up by 5. I have also worked the general rule:
- 5t-70= 10x10 grid
- 5t-63= 9x9 grid
- 5t -56= 8x8 grid
So I can work out any T Total in any sized grid which gives a T number.
