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Introduction: For this piece of GCSE math's coursework I have been asked to investigate the relationship between the total of a three-step stair on a number grid and it's position on the grid. The stair will be on a 10x10 number grid like this: 91 92 93 94 95 96 97 98 99 100 81 82 83 84 85 86 87 88 89 90 71 72 73 74 75 76 77 78 79 80 61 62 63 64 65 66 67 68 69 70 51 52 53 54 55 56 57 58 59 60 41 42 43 44 45 46 47 48 49 50 31 32 33 34 35 36 37 38 39 40 21 22 23 24 25 26 27 28 29 30 11 12 13 14 15 16 17 18 19 20 1 2 3 4 5 6 7 8 9 10 I would need to find the total for stairs on the grid. For example the one shaded in red: 45+35+25+36+26+27=194 I would then tabulate this result and move the stair one square to the right so then I would get. 46+36+26+37+27+28=200 I would then continue moving it to the right until I am unable to anymore. Part 1: I will start of in the bottom left hand corner and work myself to the right of the grid. Position 1 21 11 12 1 2 3 The total for this stair is: 21+11+1+12+2+3=50 Position 2 22 12 13 2 3 4 The total for this stair is: 22+12+2+13+3+4=56 Position 3 23 13 14 3 4 5 The total for this stair is: 23+13+3+14+4+5=62 I will now tabulate these results and others. Position Number (Lowest number in grid) 1 2 3 4 5 6 7 8 Total 50 56 62 68 74 80 86 92 From looking at my...

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