71 x 93 = 6603
73 x 91 = 6643
6603-6643= 40
The answer is 40. This means that the answer isn’t going to change.
4by4 Grid
65 66 67 68
75 76 77 78
85 86 87 88
95 96 97 98
Although this grid looks quite complicated it’s done exactly the same ways as the ones before, it’s the 4 corner numbers we are intrusted in.
65 x 98 = 6370
68 x 95 = 6460
6370-6460=90 The answer is 90.
7 8 9 10
17 18 19 20
27 28 29 30
37 38 39 40
7 x 40 = 280
10 x 37 = 370
280-370= 90
64 65 66 67
74 75 76 77
84 85 86 87
94 95 96 97
64 x 97 = 6208
67 x 94 = 6298
6208-6298= 90
The answer is again 90, this means that every 4by4 grid will give the same answer.
5by5 Grid
52 53 54 55 56
62 63 64 65 66
72 73 74 75 76
82 83 84 85 86
92 93 94 95 96
56 x 92 = 5152
52 x 96 = 4992
5152-4992 = 160
The 5by5 grid has given the overall answer as 160.
1 2 3 4 5
11 12 13 14 15
21 22 23 24 25
31 32 33 34 35
41 42 43 44 45
5 x 41 = 205
1 x 45 = 45
205-45= 160
14 15 16 17 18
24 25 26 27 28
34 35 36 37 38
44 45 46 47 48
54 55 56 57 58
18 x 54 = 972
14 x 58 = 812
972-812 = 160
the answer 160 for all of the 5by5 grids.
10by10 Grid
Grid Difference This is to show the difference between the
2by2 10 grids in the 10by10 grid.
3by3 40
4by4 90 n x n=
5by5 160
Now I am going to make a 9by9 grid and randomly select grids from it
1 2 3 4 5 6 7 8 9
10 11 12 13 14 15 16 17 18 From this 9by9 grid I am going to take a
19 20 21 22 23 24 25 26 27 2by2 grid like I did with the 10by10 grid.
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
This 2by2 grid was taken from the 9by9 grid above. We do exactly the same we did before. We are trying to find out if the answers match or if thee is a pattern.
Last time the answer was 10 lets see what the answer is now.
12 13
21 22
13 x 21 = 273
12 x 22 = 264
273-264 = 9 The answer is 9! The answer has changed because the last time I did a 2by2 grid the answer was 10. I will do some more 2by2 grids to be sure.
2by2 grid
30 31
39 40
31 x 39 = 1209
30 x 40 = 1200
1209-1200 = 9
1 2
10 11
2 x 10 = 20
1x 11 = 11
20-11= 9 The answer is again 9.
3by3 Grids
23 24 25
32 33 34
41 42 43
25 x 41 =1025
23 x 43 = 989
1025-989 = 36. The answer is 36.
1 2 3
10 11 12
19 20 21
1 x 21 = 21
3 x 19 = 57
21-57= 36 The answer is 36.
Now I am going to do a 4by4 grid.
51 52 53 54
60 61 62 63
69 70 71 72
78 79 80 81
51 x 81 = 4131
54 x 78 = 4212
4212-4131 = 81 The answer for this 4by4 grid is 81
46 47 48 49
55 56 57 58
64 65 66 67
73 74 75 76
46 x 76 = 3496
49 x 73 = 3577
3577-3496 = 81
Both of the 4by4 grids ive done produce the same answer.
Now I am going to do a 5by5 grid.
So……
28 29 30 31 32
37 38 39 40 41
46 47 48 49 50
55 56 57 58 59
64 65 66 67 68
28 x 68 = 1904
32 x 64 = 2048
1904-2048 = 144 The answer is 144.
9by9 grid
Grids Difference
2by2 9
3by3 36
4by4 81
5by5 144 n x n =
I will now continue to investigate by making a 8by8 grid.
1 2 3 4 5 6 7 8
9 10 11 12 13 14 15 16
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
From this 8by8 I am going to select a 2by2 grid.
52 53
60 61
52 x 61= 3172
53 x 60 = 3180
3172-3180= 8 The answer is 8.
56 57
64 65
56 x 65 = 3640
57 x 64 = 3648
3640-3648= 8 the answer is 8 again which means the every 2by2 grid will have the same answer.
I am now going to do a 3by3 grid.
42 43 44
50 51 52
58 59 60
42 x 60 = 2520
44 x 58 = 2552
2520-2552= 32
20 21 22
28 29 30
36 37 38
20 x 38 = 760
22 x 36 = 792
760-792 = 32 The answers again match.
Now I am going to do a 4by4.
38 39 40 41
46 47 48 49
54 55 56 57
62 63 64 65
38 x 65= 2470
41 x 62= 2542
2470-2542= 72
35 36 67 38
43 44 45 46
51 52 53 54
59 60 61 62
35 x 62 =2170
38 x 59 =2242
2170-2242 = 72 the answer is the same as before.
5by5 grid
11 12 13 14 15
20 21 22 23 24
28 29 30 31 32
36 37 38 39 40
44 45 46 47 48
11 x 48 =528
15 x 44 =660
528-660= 132
1 2 3 4 5
9 10 11 12 13
18 19 20 21 22
26 27 28 29 30
34 35 36 37 38
1 x 38= 38
5 x 34= 170
38-170= 132
Grid difference
2by2 8
3by3 32
4by4 72
5by5 132 n x n=
I will continue to investigate by making a 7by7 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
Now I am going to do a 2by2 grid using this 7by7 grid.
29 30
36 37
29x37 =1073
30x36 =1080
1073-1080=7 the answer is 7.
15 16
22 23
15 x 23= 345
16 x 22= 352
345-352= 7 The answer is again 7 which means the all the 2by2 grids in the 7by7 grid will give the same answer.
3by3 grids
31 32 33
38 39 40
45 46 47
31 x 47=1457
33 x 45=1485
1457-1485= 28
29 30 31
36 37 38
43 44 45
29 x 45=1305
31 x 43=1333
1305-1333=28 The answer is the same as before 28.
Now I am going to do a 4by4 grid.
11 12 13 14
18 19 20 21
25 22 23 24
32 33 34 35
11 x 35 = 385
14 x 32 = 448
297-448= 63
22 23 24 25
29 30 31 32
36 37 38 39
43 44 45 46
22 x 46 =1012
25 x 43 =1075
1012-1075=63
Now I am going to o a 5by5 grid.
15 16 17 18 19
22 23 24 25 26
39 30 31 32 33
36 37 38 39 40
43 44 45 46 47
15 x 47= 705
19 x 43= 817
705-817= 112
17 18 19 20 21
24 25 26 27 28
31 32 33 34 35
38 39 40 41 42
45 46 47 48 49
17 x 49= 833
21 x 45=945
833-945= 112 The answer remains the same.
Grid difference
2by2 7
3by3 28
4by4 63
5by5 112 n x n=
How did I get my rule?
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
