investigation into T-shapes

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investigation into T-shapes

Looking at the 9-9 grid below and the T-shape drawn on it,

The total number of the numbers on the inside of the T-shape is called the T-total

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

82 83 84 85 86 87 88 89 90

The t-total for this T-shape is:

1+2+3+11+20=37

So 37 = T-total

The number at the bottom is the T-number, So the T-number for this shape is 20

Aims:

1) Investigate the relationship between the T-total and the T-number

2) Use the grids of different sizes. Translate the T-shape to different positions. Investigate relationships between the T-total and the T-number