When you get the T-shape like this you can see that the centre numbers always go up by 9’s because of the table size, with the table set out like this a formula can be worked out to find the formula to find any T-Total on this size grid. This can be achieved by using this below:
T-Total =A
T-Number =N
T-total = N-19+N-18+N-17+N-9+N
So the formula for this grid is: 5N-63
The Testing Process for grid 9x9:
Testing the formula can be done using the variables A and N.
T-Total =A
T-Number =N
(I have used the number 5 in the formula to multiply N because there are 5 grid boxes in one T shape on any grid)
(Example T-number = 20)
A = 5N-63
N = 20
A = 5x20
= 100-63 = 37
I will now test to see if this will work any were on the 9x9 grid.
N=43
A=5x43 24+25+26+34+43=152
A=215-63
A=152
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N=49
A=5x49 30+31+32+40+49=182
A=245-63
A=182
I have fully tested the formula for three different T-numbers and the formula works any were correctly on a 9 by 9 grid.
The full formula for this size grid is: A=5N-63
6 By 6 Grid:
If you take the other numbers in the T-Shape away from the T-Number you get a T-Shape like this.
T-Total =A
T-Number =N
When you get the T-shape like this you can see that the centre numbers always go up by 6’s because of the table size, with the table set out like this a formula can be worked out to find the formula to find any T-Total on this size grid. This can be achieved by using this below:
T-Total = N-13+N-12+N-11+N-6+N
= 5N-42
The Testing Process for grid 6x6:
Testing the formula can be done using the variables A and N.
T-Total =A
T-Number =N
(I have used the number 5 in the formula to multiply N because there are 5 grid boxes in one T shape on any grid)
A = 5N-42
N = 14
A = 5x14
= 70-42 = 28
I will now test to see if this will work any were on the 6x6 grid.
N=22
A=5x22 9+10+11+16+22=68
A=110-42
A=68
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N=35
A=5x35 22+23+24+29+35=133
A=175-42
A=113
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N=32
A=5x32 19+20+21+26+32=118
A=160-42
A=118
I have fully tested the formula for three different T-numbers and the formula works any were correctly on a 6 by 6 grid.
The full formula for this size grid is: A=5N-42
