Mathematics Coursework
Number Grid
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99
00
Using 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 top right numbers in the square. Calculate the difference between these numbers.
I N V E S T I G A T E!!!!
I am going to work out a formula to work out the difference between the top right and bottom left numbers, and top left and bottom right numbers.
I will work out the difference to many different sized number squares with in the grid.
I will change the shape of the number pattern and I will also change the size of the number grid itself.
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
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61
62
63
64
65
66
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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 the original number grid.
What I will do is pick out random numbers in a square this is a two by two pattern.
2
3
22
23
I am going to multiply the top right and bottom left numbers together and the top left and bottom right numbers together.
2 x 23 = 276
3 x 22 = 286
I am going to then work out the difference between these two numbers.
286
- 276
10
By looking at this I can see I have come to the difference of 10.
I am going to take a couple of more 2 by 2 square and check to see if the difference is equal.
89
90
99
00
89 x 100 = 8900
> 10
90 x 99 = 8910
53
54
63
64
53 x 64 = 3392
> 10
54 x 63 = 3402
47
48
57
58
47 x 58 = 2726
> 10
48 x 57 = 2736
I have tried a couple more and I have came up consistently with the difference as being 10.
I can check this by a simple grid.
n
n+1
n+10
n+11
I have written a grid above. Now I take the sum:
N and N+11 and write it as a sum and then N+10 and N+1and write this as a sum.
N(N+11) = N²+11N
(N+10)(N+1) = N²+10N+1N+10
Then subtract these two together and the number I am left with should be the difference.
N²+11N
- N²+11N+10 =
10
I am left with 10 which is my difference for 2 by 2. I can do this with all my patterns but the numbers will change depending on the number pattern and grid size.
I am now going to try 3 by 3 square patterns.
Number 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
Using 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 top right numbers in the square. Calculate the difference between these numbers.
I N V E S T I G A T E!!!!
I am going to work out a formula to work out the difference between the top right and bottom left numbers, and top left and bottom right numbers.
I will work out the difference to many different sized number squares with in the grid.
I will change the shape of the number pattern and I will also change the size of the number grid itself.
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 the original number grid.
What I will do is pick out random numbers in a square this is a two by two pattern.
2
3
22
23
I am going to multiply the top right and bottom left numbers together and the top left and bottom right numbers together.
2 x 23 = 276
3 x 22 = 286
I am going to then work out the difference between these two numbers.
286
- 276
10
By looking at this I can see I have come to the difference of 10.
I am going to take a couple of more 2 by 2 square and check to see if the difference is equal.
89
90
99
00
89 x 100 = 8900
> 10
90 x 99 = 8910
53
54
63
64
53 x 64 = 3392
> 10
54 x 63 = 3402
47
48
57
58
47 x 58 = 2726
> 10
48 x 57 = 2736
I have tried a couple more and I have came up consistently with the difference as being 10.
I can check this by a simple grid.
n
n+1
n+10
n+11
I have written a grid above. Now I take the sum:
N and N+11 and write it as a sum and then N+10 and N+1and write this as a sum.
N(N+11) = N²+11N
(N+10)(N+1) = N²+10N+1N+10
Then subtract these two together and the number I am left with should be the difference.
N²+11N
- N²+11N+10 =
10
I am left with 10 which is my difference for 2 by 2. I can do this with all my patterns but the numbers will change depending on the number pattern and grid size.
I am now going to try 3 by 3 square patterns.