Patterns
I have noticed that the T- Number’s and the T-Total’s are linked. To get from 47 to 52 to 57 to 62 in the T-Total column, I have to plus 5.
If you called the T-Number “N” and call the T-Total “T”. You can make an equation:
T = 5N. But if you try that e.g. T = 5 x 22 that would equal 110. That is far too much so to get 110 down to what it should be we must subtract 63.
Therefore the equation must be:
T = 5N – 63.
I can now try this equation out on any number to show that it works.
T= 5x26 – 63
T= 67
I will show this on a number graph to show that the equation works:
If we add up the numbers in the T, it should add up to 67.
7 + 8 + 9 + 17 +26 = 67
This shows that the equation works.
Also there is another way of finding out if the equation works.
If you call the T-Total ‘N’ then the number above that, would be N – 9 and so on. I will show this on a diagram:
N – 19 N – 18 N – 17
N – 9
N
If you then put the numbers from the T, (N-19) + (N-18) + (N-17) + (N-9) + (N) = 5N – 63.
This is another way of showing that the equation works.
I will now do the same only this time I will change my grid size from 9 to 10 across. This is to see if there is a pattern.
T-Number = 22
T-Total = 40
T-Number = 23
T-Total = 45
T-Number = 24
T-Total = 50
T-Number = 25
T-Total = 55
This is a table of my results:
Because the T-Total is going up in fives I know that it is T = 5N.
5 x 22 = 110
This does not fit so if you take 70 away from 110. That fits.
Therefore the equation must be: T= 5N -70
To prove this equation works, I will use another way to show it.
N -19 N – 20 N - 21
N – 10
N
If you then put the numbers from the T, (N-21) + (N-19) + (N-20) + (N-10) + (N) = 5N – 70.
I will now change the grid from 10 to 11. Everything else will stay the same.
T-Number = 24
T-Total = 43
T-Number = 25
T-Total = 48
T- Number = 26
T- Total = 53
T- Number = 27
T- Total = 58
This is my table of results:
Because the T-Total is going up in fives I know that it is T = 5N.
5 x 24 = 120
This does not fit so if you take 72 away from 120. That fits.
Therefore the equation must be: T= 5N -72
To prove this equation works, I will use another way to show it.
N - 21 N - 22 N -23
N - 11
N
If you then put the numbers from the T, (N-11) + (N-22) + (N-23) + (N-21) + (N) = 5N – 72.
This is another way of showing that the equation works.
I will now do the same, expect the grid size will be 12 instead of 11.
