T-Totals.Plan: Part 1 I will investigate the relationship between the T-total and the T-number on a 9x9 grid. Part 2 I will investigate the relationship between the T-total, T-number and grid size.

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T - Totals Investigation


T-Totals

Introduction:

        This is an investigation on T-totals. By starting with a 9x9 grid, and numbering it, so the top left corner numbered with one and work downwards. An example of the grid is shown below.

The investigation will be done with a standard T-shape which is 3 along and from the centre 2 more down. As shown below.

This is the t-number for a T-shape.

The T-total is all the numbers in the T-shape added together. The T-total for this specific example is: 2+3+4+12+21=42.

Plan:

        Part 1 – I will investigate the relationship between the T-total and the  T-number on a 9x9 grid.

        Part 2 – I will investigate the relationship between the T-total, T-number and grid size.

Part 1:

        Diagrams:

        

           20+21+22+30+39=132                             52+53+54+62+71=292

         T-total = 132                                    T-total = 292

                        

                                      4+5+6+14+23=52

                                        T-total = 52

From now on:

        Let T-total be T!

        Let T-number be n!

Now I have shown some examples, a table is required so the formula can be solved between the relationship of the T and n for a 9x9 grid.

                        n                                T

                        1                                X

                                                        X

                        19                                X        

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                        20                                37

                        21                                42

                        22                                47

                        23                                52

24                                57

                        25                                62

        26                                67

        27                                X

28                                X

        29                                82

        38                                127

80                                337

As I was writing out the table I noticed that as n increased by one T also increased by 5. This has happened because each time the T-number is increased by one, all 5 boxes in the T-shape move along one too.

        The formula:

n = T-number        20        21        22        23        24        25

T = T-total                 37        42        47        52        57        62

                        

From this I can see that the formula will have 5n in because there is a difference of 5 each time for T as n is increased by 1. Also all 5 boxes ...

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