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Higher Tier Task - 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 Use the following rule: find the product of the top left number and the bottom right number in the square. Do the same thing with the bottom left and the top right numbers in the square. Calculate the difference between these numbers. INVESTIGATE! I will begin with 2x2 windows on a 10x10 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 34 x 25 = 850 49 x 58 = 2842 24 x 35 = 840- 48 x 59 = 2832- 10 10 88 x 97 = 8536 63 x 72 = 4536 87 x 98 = 8526- 73 x 62 = 4526- 10 10 3 x 12 = 36 6 x 15 = 90 2 x 13 = 26- 5 x 16 = 80- 10 10 For all of these windows you can see that the difference is always 10, so anywhere you put a 2x2 window on a 10x10 grid you will...

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