To prove that the patterns work anywhere within the grid I am testing it at a different point within the grid. The T-numbers I will test it with is 56 and 65. If my patterns are work at any point in the grid, than the difference between both results should be 45. Therefore I predict the T-Total for the T-Number 56 should be 217, and the T-total for the T-number 65 should be 262 if the pattern follows.
The results above of the predictions made earlier as to what the T-Total should be if the
T-Number was 56 and 65 prove that the pattern follows anywhere within the grid.
The values inside the T of any 9x9 grid can be expressed in an algebraic way. This is as follows with n being the value of the T-Number.
Algebraic Expression for the 9x9 grid:
Using the algebraic expressions I found a formula finding the T-Total for any T-Number inside a 9x9 grid.
The rule is:
T-Total = n+(n-9)+(n-19)+(n-18)+(n-17)
This can be simplified to:
T-Total = 5n-63
For example if n=40:
T-Total=(5x40)-63
T-Total=200-63
T-Total=137
To see if the formula is correct for this I will find the T-Total using the original method.
T-Total=21+22+24+31+40=137
T-Number=40
To establish that this expression is correct I will present further examples to show that it is correct.
If n=60:
T-Total=(5x60)-63
T-Total=300-63
T-Total=237
T-Total=41+42+43+51+60=237
T-Number=60
As the other example shows, my formula is correct as the same T-Total was found for each T-Number when using both methods.
8x8 Number grid (Across)
As the T-Shape translates across by 1, the T-Number increases by 1. The difference in T-Total is 5 each time so far. Therefore the T-Total for the T-Number 22 should be 54 if the pattern follows. The T-Total for the T-Number 23 should be 59.
The results show the predictions made earlier are correct proving that the pattern follows
8x8 Square Grid patterns down
I have noticed patterns within my table of results. One of the patterns I have noticed is, as the T-Shape translates down by 1, the T-Number increases by 8, which is also the size of the grid. Another noticeable pattern is the T-Total difference is 40 each time.
To prove that the patterns work anywhere within the grid I am testing it at a different point within the grid. The T-numbers I will test it with is 50 and 58. If my patterns are work at any point in the grid, than the difference between both results should be 45. Therefore I predict the T-Total for the T-Number 56 should be 194, and the T-total for the T-number 58 should be 232 if the pattern follows.
The results above of the predictions made earlier as to what the T-Total should be if the
T-Number was 56 and 65 prove that the pattern follows anywhere within the grid.
The values inside the T shape of any 8x8 grid can be expressed in an algebraic way. This follows with n being the value of the T-Number.
Algebraic expression for a 8x8 grid:
Using the algebraic expressions I found a formula finding the T-Total for any T-Number inside an 8x8 grid.
The rule is:
T-Total = n+(n-8)+(n-17)+(n-16)+(n-15)
This can be simplified to:
T-Total = 5n-56
For example if n=36:
T-Total=(5x36)-56
T-Total=180-56
T-Total=124
To see if the formula is correct for this I will find the T-Total using the original method.
T-Total=19+20+21+28+36=124
T-Number=36
To establish that this expression is correct I will present further examples to show that it is correct.
If n=44:
T-Total=(5x44)-56
T-Total=220-56
T-Total=164
T-Total=27+28+29+36+44=164
T-Number=44
As the other example shows, my formula is correct as the same T-Total was found for each T-Number when using both methods.
10x10 Number grid (Across)
As the T-Shape translates across by 1, the T-Number increases by 1. The difference in T-Total is 5 each time so far. Therefore the T-Total for the T-Number 26 should be 60 if the pattern follows. The T-Total for the T-Number 27 should be 65.
The results show the predictions made earlier are correct proving that there is a pattern.
10x10 Square Grid patterns down
I have noticed patterns within my table of results. One of the patterns I have noticed is, as the T-Shape translates down by 1, the T-Number increases by 10. Another noticeable pattern is the T-Total difference is 50 each time.
To prove that the patterns work anywhere within the grid I am testing it at a different point within the grid. The T-numbers I will test it with is 62 and 72. If my patterns are work at any point in the grid, than the difference between both results should be 50. Therefore I predict the T-Total for the T-Number 62 should be 240, and the T-total for the T-number 72 should be 290 if the pattern follows.
The results above of the predictions made earlier as to what the T-Total should be if the
T-Number was 62 and 72 prove that the pattern follows anywhere within the grid.
The values inside the T of any 10x10 grid can be expressed in an algebraic way. This is as follows with n being the value of the T-Number.
Algebraic expression for a 10x10 grid:
Using the algebraic expressions a formula can be found so the
T-Total for any T-Number inside an 10x10 grid could be found straight away. The rule is:
T-Total = n+(n-10)+(n-21)+(n-20)+(n-19)
This can be simplified to:
T-total = 5n – 70
For example if n=82:
T-Total=(5x82)-70
T-Total=410-70
T-Total=340
To see if the formula is correct for this I will find the T-Total using the original method.
T-Total=82+72+61+62+63=340
T-Number=82
To establish that this expression is correct I will present further examples to show that it is correct
If n=92:
T-Total=(5x92)-70
T-Total=460-70
T-Total=390
T-Total=71+72+73+82+92=390
T-Number=92
As the other example shows, my formula is correct as the same T-Total was found for each T-Number when using both methods.
9x9 Grid Rotations: