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Number Grid Coursework
I am going to investigate number grids for my mathematical coursework. I will begin by producing a 10 by 10 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 82 83 84 85 86 87 88 89 90
91 92 93 94 95 96 97 98 99 100
I am now going to investigate five 2 by 2 boxes by multiplying the top right number by the bottom left number in each box. I will then apply the same method to the two remaining numbers in each box by multiplying the top left number by the bottom right number. ...
N N+1 N+2 N+3
N+10 N+11 N+12 N+13
N+20 N+21 N+22 N+23
N+30 N+31 N+32 N+33
TR x BL - (N + 3) (N + 30) TL x BR - N(N + 33)
= N² + 30N + 3N +90 = N² + 33N
= N² 33 N + 90
TR x BL – (TL x BR) - N² + 33N + 90 – (N² + 33N)
= 90
N N+1 N+2 N+3 N+4
N+10 N+11 N+12 N+13 N+14
N+20 N+21 N+22 N+23 N+24
N+30 N+31 N+32 N+33 N+34
N+40 N+41 N+42 N+43 N+44
TR x BL - (N + 4) (N + 40) TL x BR - N(N + 44)
= N² + 40N + 4N + 160 = N² + 44N
= N² + 44N +160
TR x BL – (TL x BR) - N² + 44N + 160 – (N² +44N)
= 160
The answer to TR x BL – (TL x BR) will always be the same in a 10 by 10 number grid if the number boxes are the same size.
Approximate Word count = 1221
Approximate Pages = 4.9
(250 words per page double spaced)
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