44 45 46
54 55 56
34x56 = 1904
54x36 = 1944
The Difference is of 40 because 1944 – 1904
This shows me that a 3x3 grid will always have a difference of 40 and if I continued doing a 3x3 grid sequence I would always get a difference of 40, if I use algebra to work out the difference I also get 40 as the answer as shown above.
4x4 Grids
1.
12 13 14 15
22 23 24 25
32 33 34 35
42 43 44 45
12x45 = 540
42x15 = 630
The Difference is 90 because 630 – 540
2.
23 24 25 26
33 34 35 36
43 44 45 46
53 54 55 56
23x56 = 1288
26x53 = 1378
The Difference is 90 because 1378 – 1288
3.
34 35 36 37
44 45 46 47
54 55 56 57
64 65 66 67
34x67 = 2278
64x37 = 2368
The Difference is 90 because 2368 – 1378
This shows me that a 4x4 grid will always have a difference of 90 and if I continued doing a 4x4 grid sequence I would always get a difference of 90, if I use algebra to work out the difference I also get 90 as the answer as shown above.
If I continue to use algebra to show my difference I will always get the answer I have found from multiplying the corner numbers and subtract the answers.
5x5 Grids
1.
12 13 14 15 16
22 23 24 25 26
32 33 34 35 36
42 43 44 45 56
52 53 54 55 56
12x56 = 672
16x52 = 832
The Difference is 160 because 832 – 672
2.
34 35 36 37 38
44 45 46 47 48
54 55 56 57 58
64 65 66 67 68
74 75 76 77 78
34x78 = 2652
74x38 = 2812
The Difference is 160 because 2812 – 2652
3.
45 46 47 48 49
55 56 57 58 59
65 66 67 68 69
75 76 77 78 79
85 86 87 88 89
45x89 = 4005
85x49 = 4165
The Difference is 160 because 4165 – 4005
This shows me that a 5x5 grid will always have a difference of 160 and if I continued doing a 5x5 grid sequence I would always get a difference of 160.
6x6 Grids
1.
15 16 17 18 19 20
25 26 27 28 29 30
35 36 37 38 39 40
45 46 47 48 49 50
65 66 67 68 69 70
15x70 = 1050
20x65 = 1300
The Difference is 250 because 1300 - 1050
2.
23 24 25 26 27 28
33 34 35 36 37 38
43 44 45 46 47 48
53 54 55 56 57 58
63 64 65 66 67 68
73 74 75 76 77 78
23x78 = 1794
28x73 = 2044
The Difference is 250 because 2044 - 1794
3.
42 43 44 45 46 47
52 53 54 55 56 57
62 63 64 65 66 67
72 73 74 75 76 77
82 83 84 85 86 87
92 93 94 95 96 97
42x97 = 4074
47x92 = 4324
The Difference is 250 because 4324 - 4074
This shows me that a 6x6 grid will always have a difference of 250 and if I continued doing a 6x6 grid sequence I would always get a difference of 250.
7x7 Grids
1.
01 02 03 04 05 06 07
11 12 13 14 15 16 17
21 22 23 24 25 26 27
31 32 33 34 35 36 37
41 42 43 44 45 46 47
51 52 53 54 55 56 57
61 62 63 64 65 66 67
1x57 = 57
61x7 = 427
The Difference is 370 because 427 – 57
2.
12 13 14 15 16 17 18
22 23 24 25 26 27 28
32 33 34 35 36 37 38
42 43 44 45 46 47 48
52 53 54 55 56 57 58
62 63 64 65 66 67 68
72 73 74 75 76 77 78
12x78 = 936
18x72 = 1296
The Difference is 360 because 1296 – 936
3.
23 24 25 26 27 28 29
33 34 35 36 37 38 39
43 44 45 46 47 48 49
53 54 55 56 57 58 59
63 64 65 66 67 68 69
73 74 75 76 77 78 79
83 84 85 86 87 88 89
23x89 = 2047
29x83 = 2407
The Difference is 360 because 2407 – 2047
This shows me that a 7x7 grid will always have a difference of 360 and if I continued doing a 2x2 grid sequence I would always get a difference of 360.
Number Grid.
I had tried the formula 10N2 and it did not work so I then changed it to 10(N-1) 2 and it worked because with 10N2 it was one Nth term in front and when I took away one Nth term it left me with the correct answer.
I can now find the rest of the sequence with this formula here are 3 examples used with the formula
Here are my examples;
Here is the evidence backing up my formula.
8x8 Grid.
22x99 = 2178
29x92 = 2668
This gives me the answer of 490 because 2669 - 2668
9x9 Grid
11x99 = 1089
19x91 = 1729
This gives me the answer of 640 because 1729 - 1089
10x10 Grid
01x100 = 100
10x91 = 910
This gives me the answer of 810 because 910 – 100
This shows that there is a sequence to the number grids, and it works with the formula I have found.
Also it shows my hypothesis was correct as each grid size had a pattern of a difference of ten.
