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

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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