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Number Stairs Investigation 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 lowest number (n) Long operation Total (t) 1st Difference (D0) 1 1 + 2 + 3 + 11 + 12 + 21 50 6 2 2 + 3 + 4 + 12 + 13 + 22 56 6 3 3 + 4 + 5 + 13 + 14 + 23 62 6 4 4 + 5 + 6 + 14 + 15 + 24 68 6 5 5 + 6 + 7 + 15 + 16 + 25 74 6 Judging by this, the first part of the overall equation for a 3 step stair is 6n +? n 6n T D0 1 6 50 44 2 12 56 44 3 18 62 44 4 24 68 44 5 30 74 44 This shows the difference between 6n and T as + 44 Therefore the equation for a 3 step stair on a 10x10 grid is 6n + 44 The same sequence can be used for a 4 step stair lowest number (n) Long operation Total (t) 1st Difference (D0) 1 1 + 2 + 3 + 4 + 11 + 12 + 13 + 21 + 22 + 31 120 10 2 2 + 3 + 4 + 5 + 12 + 13 + 14 + 22 +...

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