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Number Grids The diagram shows a 10*10 grid, a rectangle has been shaded on the 10*10 grid. I will find the diagonal difference between the products of the numbers in the opposite corners of the rectangle. 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 Opposite numbers in the rectangle are:- 54 and 66 56 and 64 56*64=3584 54*66=3564 .·. The Diagonal Difference = 3584 - 3564 = 20 Study I have studied some more 3*2 rectangles and I have found this:- 12 13 14 22 23 24 12*24=288 14*22=308 Diagonal difference =308 - 288=20 74*86=6364 76*84=6384 Diagonal difference =6384 - 6364=20 74 75 76 84 85 86 27*39=1053 29*37=1073 Diagonal difference =1073 - 1053= 20 27 28 29 37 38 39 So from this I conclude that all 3*2 rectangles have a diagonal difference of 20. After doing this I wondered if this theory would work if I used a 2*3 rectangle. 27*48=1296 28*47=1316 Diagonal difference=1316 - 1296=20 27 28 37 38 47 48 34*55=1870 35*54=1890 Diagonal difference=1890 - 1870=20 34 35 44 45 54 55 So I then from this I wondered if larger rectangles had the same diagonal difference from this I found: - Rectangle Rows * columns Diagonal difference 2*3 20 3*4 60 4*5 120 5*6 200 6*7 300 7*8 420 From this I will try to find a formula: - Rectangle Rows * columns Diagonal difference This goes up in tens...

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