Rule: +5 on to the answer.
I use my 8 x 8 grid again but this time I use my “T” shape to go down, and see if I can spot the pattern for my T-total…
Total= 9+10+11+18+26=74
(T number= 26)
Total= 17+18+19+26+34=114
(T number= 34)
Total= 25+26+27+34+42=154
(T number= 42)
I search for a pattern in the total numbers and write down the rule:
Rule: +40 on to the answer.
7 x 7 Grid
I have a 7 x 7 grid that I will use to find the pattern for the T-total by moving the “T” shape, across the grid (right) …
Total= 1+2+3+9+16= 31
(T number= 16)
Total=2+3+4+10+17=36
(T number=17)
Total=3+4+5+11+18=41
(T number=18)
I search for a pattern in the total numbers and write down the rule:
Rule: +5 on to the answer.
I use my 7 x 7 grid again but this time I use my “T” shape to go down, and see if I can spot the pattern for my T-total…
Total=8+9+10+16+23-66
(T number=23)
Total=15+16+17+23+30=101
(T number=23)
Total=22+23+24+30+37=136
(T number=37)
I search for a pattern in the total numbers and write down the rule:
Rule: +44 on to the answer.
Moving the “T” shape across, right…
9 X 9 => +5
8 x 8 => +5
7 x 7 =>+5
I have found out in the pattern of different grid sizes that it doesn’t affect the pattern if the grid size changes.
Moving the “T” shape downwards…
9 X 9 => +45 - 5
8 x 8 => +40
7 x 7 =>+35 -5
Algebra
9 x 9 grid
Total= t +(t-9) + (t-19)
+ (t-18) + (t-17)
= 5T - 63
8 x 8 Grid
Total= t + (t-8) + (t – 17)
+ (t-16) + (t-15)
=5t- 56
7 x 7 Grid
Total= t + (t-7) + (t-15)
+ (t-14) + (t-13)
= 5t – 49
Algebra
(9 x 9) T = 5t – 63 = 5t – 7x 9
(8 x 8) T = 5t – 56 = 5t – 7 x 8
(7 x 7) T = 5t – 49 = 5t – 7 x 7
T= 5t – 7
T= T-number
G= Grid size
T= T-total
Rotation
Across
I have a 9 x 9 grid that I will draw a “T” shape on.
To which I will rotate 90 degree clockwise. I will then write down the numbers inside the shape to find out the pattern…
Total= 3+12+21+11+10= 57
(T-number= 10)
Total= 4+13+22+12+11= 62
(T-number= 47)
Total= 5+14+23+13+12=67
(T-number= 12)
Rule: + 5
I found out that when I move my rotated 90 “T” shape to the right I add on 5 to the answer.
I use the same 9x9 grid and draw the same rotated “T” shape but this time going down.
Total= 19+20+21+12+30=102
(T-number=19)
Total= 28+29+30+21+39=147
(T-number=28)
Total= 37+38+39+30+48=192
(T-number=37)
Rule: +45
I found out that when I move my rotated 90 “T” shape downwards I add on 45 to the answer.
Algebra
Total= t+ (t+1) + (t-1) +
(t+2) + (t+11)
=5t+7
Across
I have an 8 x 8 grid that I will draw a “T” shape on.
To which I will rotate 90 degrees clockwise. I will then write down the numbers inside the shape to find out the pattern…
Total=9+10+11+3+19=52
(T-number=9)
Total=10+11+12+4+20=57
(T-number=10)
Total=11+12+13+5+21=62
(T-number=11)
Rule: + 5
I found out that when I move my rotated 90-degree “T” shape to the right I add on 5 to the answer.
I use the same 8x8 grid and draw the same rotated “T” shape but this time going down.
Total=9+10+11+3+19+52
(T-number=9)
Total=17+18+19+11+27+92
(T-number=17)
Total=25+26+27+19+35+132
(T-number=132)
Rule: +40
I found out that when I move my rotated 90-degree “T” shape downwards I add on 45 to the answer.
Algebra
Total=t+(t+1) + (t+2) +
(t-6) + (t+10)
=5t+7
Across
I have a 7 x 7 grid that I will draw a “T” shape on.
To which I will rotate 90 degree clockwise. I will then write down the numbers inside the shape to find out the pattern…
Total=8+9+10+3+17=47
(T-number=8)
Total+9+10+11+4+18=52
(T-number=9)
Total=10+11+12+5+19=57
(T-number=10)
Rule: + 5
I found out that when I move my rotated 90 “T” shape to the right I add on 5 to the answer.
I use the same 7x7 grid and draw the same rotated “T” shape but this time going down.
Total=8+9+10+3+17=47
(T-number=8)
Total=15+16+17+10+24=82
(T-number=15)
Total+22+23+24+17+31=117
(T-number=22)
Rule: +35
I found out that when I move my rotated 90-degree “T” shape downwards I add on 35 to the answer.
Algebra
Total=t+ (t+1) + (t+2) +
(t-5) + (t+9)
=5t+7
Algebra
9x9 Grid
Total=t+(t+1) + (t+2) +
(t-7) + (t+11)
=+5t+7
8x8 Grid
Total=t+(t+1) + (t+2) +
(t-6) + (t+10)
=5t+7
7x7 Grid
Total=t+(t+1) + (t+2) +
(t-5) = (t+6)
+5t+7
(9x9) Total= 5t+7=5t
(8x8) Total=5t+7=5t
(7x7) Total=5t+7=5t
T= 5t+7
T= t=number
G= Grid size
T= T=total
I have a 9 x 9 grid that I will draw a “T” shape on.
To which I will rotate 180 degree clockwise. I will then write down the numbers inside the shape to find out the pattern…
Across
Total=2+11+20+21+19=73
(T-number=2)
Total=3+12+21+22+20=78
(T-number=3)
Total+4+13+22+23+21+83
(T-number+4)
Rule=+5
I found out that when I move my rotated 180-degree “T” shape across I add on 5 to the answer.
I use the same 9x9 grid and draw the same rotated “T” shape but this time going down.
Total=2+11+20+21+19=78
(T-number=2)
Total=11+20+29+30+28+118
(T-number=11)
Total=20+29+38+39+37=163
(T-number=20)
Rule: +40
I have found out that when I move my rotated 180degree “T” shape downwards I add on 40 to the answer.
Algebra
Total=t+ (t+9) + (t+18) +
(t+19) + (t+17)
=5t+63
Across
I have an 8 x 8 grid that I will draw a “T” shape on.
To which I will rotate 180 degree clockwise. I will then write down the numbers inside the shape to find out the pattern…
Total=2+10+18+17+19=66
(T-number=2)
Total=3+11+19+18+20=71
(T-number=3)
Total=4+12+20+19+21=76
(T-number=4)
Rule: +5
I found out that when I move my rotated 180 “T” shape across I add on 5 to the answer.
I use the same 8x8 grid and draw the same rotated “T” shape but this time going down.
Total=2+10+18+17+19=66
(T-number=2)
Total=10+18+26+25+27=106
(T-number=10)
Total=18+26+34+33+35=146
(T-number=18)
Rule: +40
I have found out that when I move my rotated 180 “T” shape downwards I add on 40 to the answer.
Algebra
Total= t+ (t+8) = (t+15) +
(t+16) + (t+17)
=5t+56
Across
I have a 7 x 7 grid that I will draw a “T” shape on.
To which I will rotate 180 degree clockwise. I will then write down the numbers inside the shape to find out the pattern…
Total=2+9+16+17+15=59
(T-number=2)
Total=3+10+17+16+18=64
(T-number=3)
Total=4+11+18+19+17=69
(T-number=4)
Rule: +5
I found out that when I move my rotated 180 “T” shape across I add on 5 to the answer.
I use the same 7x7 grid and draw the same rotated “T” shape but this time going down.
Total=2+9+16+17+15=59
(T-number=2)
Total=9+16+23+22+24=94
(T-number=9)
Total=16+23+30+29+31=129
(T-number=16)
Rule: +35
I have found out that when I move my rotated 180 “T” shape downwards I add on 35 to the answer.
Algebra
Total= t+ (t+7) + (t+14) +
(t+13) + (t+15)
=5t+49
Algebra
9x9 Grid
Total= t+ (t+9) + (t+18) +
(t+19) + (t+17)
+5t+63
8x8 Grid
Total= t+ (t+8) + (t+16) +
(t+17) + (t+15)
=5t+56
7x7 Grid
Total= t+(t+7) + (t+14) +
(t+15) + (t+13)
=5t+49
(9x9) Total= 5t+63=5t+7x9
(8x8) Total=5t+56=5t+7x8
(7x7) Total=5t+49=5t+7x7
T= 5t+7xG
T= t=number
G= Grid size
T= T=total
I have a 9 x 9 grid that I will draw a “T” shape on.
To which I will rotate 90 degrees anti-clockwise. I will then write down the numbers inside the shape to find out the pattern…
Across
Total=12+11+10+1+19=53
(T-number=12)
Total=13+12+11+2+20=58
(T-number=13)
Total=14+13+12+3+21=63
(T-number=14)
Rule: +5
I found out that when I move my rotated 90 degrees anti-clockwise “T” shape across I add on 5 to the answer.
I use the same 9x9 grid and draw the same rotated “T” shape but this time going down.
Total=30+29+28+19+37=143
(T-number=30)
Total=39+38+37+28+46=188
(T-number=39)
Total=48+47+46+37+46=243
(T-number=48)
Rule: +45
Algebra
Total= t+ (t-1) + (t-2) +
(t-11) +(t+7)
= 5t-7
I have an 8 x 8 grid that I will draw a “T” shape on.
To which I will rotate 90 degrees anti-clockwise. I will then write down the numbers inside the shape to find out the pattern…
Across
Total=11+10+9+1+17=48
(T-number11)
Total=12+11+10+2+18=53
(T-number=12)
Total=13+12+11+19+3=58
(T-number=13)
Rule: +5
I found out that when I move my rotated 90 degree anti-clockwise “T” shape across I add on 5 to the answer.
I use the same 8x8 grid and draw the same rotated “T” shape but this time going down.
Total=11+10+9+1+17=48
(T-number11)
Total=19+18+17+25+9=88
(T-number=19)
Total=27+26+25+17+33=128
(T-number=27)
Rule: +40
I have found out that when I move my rotated 90 anti-clockwise “T” shape downwards I add on 40 to the answer.
Algebra
Total= t+ (t-1) + (t-2) +
(t-10) + (t+6)
=5t-7
I have a 7 x 7 grid that I will draw a “T” shape on.
To which I will rotate 90 degree anti-clockwise. I will then write down the numbers inside the shape to find out the pattern…
Across
Total= 10+9+8+15+1=43
(T-number=10)
Total= 11+10+9+16+2=48
(T-number=11)
Total=12+11+10+17+3=53
(T-number=12)
Rule: +5
I found out that when I move my rotated 90 anti-clockwise “T” shape across I add on 5 to the answer.
I use the same 7x7 grid and draw the same rotated “T” shape but this time going down.
Total=10+9+8+15+1=43
(T-number=10)
Total=17+16+15+22+8=78
(T-number=17)
Total=24+23+22+29+15=113
(T-number=24)
Rule: +35
I have found out that when I move my rotated 90 anti-clockwise “T” shape downwards I add on 35 to the answer.
Algebra
Total= t+ (t-1) + (t-2) +
(t-9) + (t+5)
=5t-7
Algebra
9x9 Grid
Total= t+ (t-1) + (t-2) +
(t-11) + (t+7)
=5t-7
8x8 Grid
Total= t+ (t-1) + (t-2) +
(t-10) + (t+6)
=5t-7
7x7 Grid
Total= t+(t-1) + (t-2) +
(t-10) + (t+6)
=5t-7
(9x9) Total= 5t-7=5t-7
(8x8) Total=5t-7=5t-7
(7x7) Total=5t-7=5t-7
T= 5t-7
T= t=number
G= Grid size
T= T=total
Translation & Rotation
9x9 Grid
T = total
M= more
8x8 Grid
T=Total
A=Answer
7x7 Grid
T=Total
A=Answer
Extension
For my extension task, what I could do to extend my work could be to invent an algebra equation for a rotated “T” moving left, right, up and down. For example;
← {Rotated 90-degree anti-clockwise “T” shape on a 7 7 by 7 grid}
5+12+19+13+14= 63
T=14
Rule= +5
Algebra equation: Total=14+R5 ← for each move
Conclusion
I am going to put the formulas in a table to make it easy to understand.
Explanation
In the table it shows that ‘T’ is 5t-7g (t-number) and (G= Grid size) ‘
Is 5t+7g. The symbols, which mean the opposite of each other, are the positive (+) and negative (-), when the ‘T’ us a normal ‘T’ it is negative and when it us rotated 90 clockwise the ‘
Becomes positive (+).
When the normal ‘T’ moves 90 clockwise the formula changes to T= 5t-7 and when the ‘T’ moves 90 anti-clockwise the formula becomes T= 5t+7. It is the negative (-) and positive (+).
Limitation
This course works limitations can be controlled up to probably a 20 x 20 grid. Its reduce is up to a 3x3 grid.
Improving
To improve my formula I would do more T-number examples to make sure and prove to my self that the formulae is correct.
Also re-check my numbering and grids.
