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| Topic: |
Miscellaneous
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| Number of pages / Number of words: |
17 / 4664 |
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This is due to the fact that some numbers will result in the smaller grid no longer fitting on the larger grid, rendering our formula incomplete. For example if N was 91, the bottom two squares would extend beyond the 10x10 grids boundaries.
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
As you can see we are missing the values needed with which to complete our multiplications! Therefore we know that the starting number must be positioned at least the second grid's size away from the bottom or right edges...
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I therefore predict in my next equation with the starting number of 87, that when I deduct the two totals I will be left with ten.
Therefore if N=87 87?+957= 8526
87?+957+10= 8536
87
88
97 98
87x98= 8526
97x88= 8536
This check shows that my prediction was correct.
Now that I know this about 2x2 grids I will now investigate the effect a 3x3 grid has on the same procedure...
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