Investigation of T-Shape.

Part 1

Investigate the relationship between the t-total and t-number

As you see when t-number goes up 1 the t-total goes up 5

So, ratio of t-number and t-total is 1 : 5

Another way to work out the t-total is by formula

             So, total=n+(n-9)+(n-17)+(n-18)+(n-19)

                   =5n-63

          So,   t=5n-63, when t is the t-total and n is it’s position (the bottom number)

The formula starts with 5n because the t-total rise by 5 for every t-number, and -63 works out by the difference of the t-number and another number in the t-shape. This has to be done to the other 4 numbers in the t-shape.

E.g.

 

This is where the number 63 came from in the formula.

There is also another place this 63 comes from. This is 9*7=63. The nine in this comes from the size of the grid this one been nine. If the grid size were 10 by 10 then it would be 10*7.( we will prove this in part 2)

Now here is an example of using the formula ( 5n – 63 = t-total )

5 * 25 – 63 = t-total

5 * 25 – 63 = 62

Check the answer

t-total = 6 + 7 + 8 + 16 + 25

=62

This formula works