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To investigate the relationship between the T-total and the T-number. The problem of the question is based on a 9 by 9 number grid.

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Introduction

Kimberly Wong 10F MATH COURSEWORK T-Totals Part I: Aim: To investigate the relationship between the T-total and the T-number. The problem of the question is based on a 9 by 9 number grid. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 T-shape drawn on a 9x9 grid: A T-shape is drawn on the 9 by 9 grid and all the numbers the T-shape are added together, and the sum is the T-total. This 'T-total' is known as T. The problem is to figure out the relationship between the T-total and the position of the T-shape (the position of the T-shape is the number in the bottom part of the T-shape). This position of the T-shape is known as p. ...read more.

Middle

Proving the Formula: 1. * Because it is a 9 x 9 grid, the difference between the three numbers is 9 * Each level increased means a decrease in 9 T = p (p - 9) + (p - 18) + (p - 17) + (p - 19) decrease by 9 each time This is shown in the equation. P represents the position of the T-shape, which can be shown as 0 because every other number has a relationship on some way with this number. This can be described as (9 x 0). 9 is because it is on a 9 x 9 number grid and zero is because it is the starting level of the T-shape. The next box above is (p - 9) because it has increased one level on the 9 x 9 grid, and therefore the number is 9 less than before. So, since the number is 9 less than the p number, it is therefore (p - 9). Another way I got the 9, is from (9 x 1). 9 is because it is a 9 x 9 number grid, and 1 because it has increased one level. ...read more.

Conclusion

Therefore, the equation is just p, because 8 x 0 is just 0. * 8 x 1 is because it is on an 8 x 8 number grid, and 1 is because it has increased one level. 8 x 1 is 8, but because it has increased one level, the number has decreased by 8, so it is p - 8. * 8 x 2 is because it is on an 8 x 8 number grid and 2 is because it has gone up 2 levels. 8 x 2 is 16, but because it has increased 2 levels, the number has decreased by 16, so it is p - 16. * The top two side numbers are figured out using the middle top number. Since they are consecutive, the number on the left would be p - 17 (this is found from 8 x 2 +1, and the number on the right would be p - 15 (this if found from 8 x 2 - 1). Also, since I know that T= 5p - 63, I now also know what p would be if I only knew T. If T= 5p - 63 P= T + 63 5 ...read more.

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