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My first investigation was to move the T from left to right. Starting at the top, with 91. 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 Total Stair Total 91 91+81+82+71+72+73 470 92 92+82+83+72+73+74 476 93 93+83+84+73+74+75 482 94 94+84+85+74+75+76 488 95 95+85+86+75+76+77 494 96 96+86+87+76+77+78 500 97 97+87+88+77+78+79 506 98 98+88+89+78+79+80 512 As the T is moved across from left to right, the stair total has increased by 6 every time. Left to right + 6. My second investigation was to move the T form top to bottom. Starting form the number 91. 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 Total Stair Total 91 91+81+82+71+72+73 470 81 81+71+72+61+62+63 410 71 71+61+62+51+52+53 350 61 61+51+52+41+42+43 290 51 51+41+42+31+32+33 230 41 41+31+32+21+22+23 170 31 31+21+22+11+12+13 110 21 21+11+12+1+2+3 50 As this form of the T was moved from the top to the bottom, the stair total decreased by 60 each time. Top to bottom -60 My third investigation was to move the T from left to right but as the form that is shown. Starting from 93. 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 Total Stair Total 93 93+82+83+71+72+73 474 94 94+83+84+72+73+74 480 95 95+84+85+73+74+75 486 96 96+85+86+74+75+76 492 97 97+86+87+75+76+77 498 98 98+87+88+76+77+78 504 99 99+88+89+77+78+79 510 100 100+89+90+78+79+80 516 As this reverse form of T is moved from left to right, the stair total has increased again by 6. Left to right +6 My fourth investigation was to move the T from the top to the bottom, using this form of T Starting...

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