Number Grids
The Problem
The problem is to investigate the differences of corner numbers on a multiplication grid.
Introduction
To solve this problem I will have to choose several examples of squares on a grid:
E.g. 2x2, 3x3, 4x4
To work this out I will need to take the opposite corners of the square and subtract them from the other sum of the two corners. This is easier seen in the diagram shown below:
*The RED numbers are always multiplied then subtracted from the sum of the YELLOW numbers.
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
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
00
This is an example of a 2x2 square. I will then make an equation with this:
Difference= (2x11)-(1x12)
= 10
The difference for this example is ten.
2x2 Squares
I will use on grid to use several example of 2x2 squares by placing them randomly on the grid.
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
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
00
From the squares I can find the difference for a 2x2 grid.
(2x11)-(1x12) = 10
(25x34)-(24x35) = 10
(63x72)-(62x73) = 10
(58x67)-(57x68) = 10
(90x99)-(89x100)=10
For all of these you can that the difference is a constant 10, so anywhere you put a 2x2 square on a 10x10 grid you will always get the same difference of ten. This can also be shown algebraically.
The Problem
The problem is to investigate the differences of corner numbers on a multiplication grid.
Introduction
To solve this problem I will have to choose several examples of squares on a grid:
E.g. 2x2, 3x3, 4x4
To work this out I will need to take the opposite corners of the square and subtract them from the other sum of the two corners. This is easier seen in the diagram shown below:
*The RED numbers are always multiplied then subtracted from the sum of the YELLOW numbers.
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
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
00
This is an example of a 2x2 square. I will then make an equation with this:
Difference= (2x11)-(1x12)
= 10
The difference for this example is ten.
2x2 Squares
I will use on grid to use several example of 2x2 squares by placing them randomly on the grid.
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
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
00
From the squares I can find the difference for a 2x2 grid.
(2x11)-(1x12) = 10
(25x34)-(24x35) = 10
(63x72)-(62x73) = 10
(58x67)-(57x68) = 10
(90x99)-(89x100)=10
For all of these you can that the difference is a constant 10, so anywhere you put a 2x2 square on a 10x10 grid you will always get the same difference of ten. This can also be shown algebraically.
