Investigating Patterns in Grids of Different Sizes
Introduction:
For my coursework I will be investigating patterns in grids of
different sizes. Within the grid each square has a number.
E.g.
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
For each boot (highlighted above) I will develop a formula to work out
the total value of the numbers added up. The boot will consist of
three numbers up and two across. My formula must show how to find out
the added value of the boot if placed anywhere within the grid.
Grid 5x5
========
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
I found that in grid 5x5 that the formula for the added value of the
boot is 4n+26. I discovered this by:
Working out the value of boots 1 to 4.
Boot 1= 1+6+11+12=30
Boot 2= 2+7+12+13=34
Boot 3= 3+8+13+14=38
Boot 4=4+9+14+15=42
Now I have this information I can begin to work on the sequence.
30 34 38 42
4 4 4
n
1
2
3
4
4n
4
8
12
16
Sequence
30
34
38
42
30-4=26 34-8=26 38-12=26 42-16=26
These all-equal 26!
This shows that the formula is 4n+26=v
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