Squares and columns Investigation

1 12 13 14 15 2 (2+3+7+8) = 20

6 17 18 19 20 3 (3+4+8+9) = 24

21 22 23 24 25 4 (4+5+9+10) = 28

5 (5+6+10+11) = 32

6 (6+7+11+12) = 36

7 (7+8+12+13) = 40

This is the step size

they are all going up in fours

The reason I put number 5 in as a different colour is because it doesn't really exist because its on the end row, also numbers 10, 15, 20 and 25 don't exist, they would only exist if I added another number to the end of the row, it also shows what it would be anyway so it keeps the pattern going.

The formula for the 2 x 2 square

Step size

4n + ? = 36

4 x 6 = 24 + ? = 36

? = 12

To prove that the formula is correct I will do the next two squares in the sequence numbers 8 and 9.

Square name 8

4 x 8 = 32

32 + 12 = 44

Square name 9

4 x 9 = 36

36 + 12 = 48

I am now going to do a 3 x 3 square inside a 5 x 5 square and get the formula.

1 2 3 4 5

6 7 8 9 10

1 12 13 14 15

6 17 18 19 20

21 22 23 24 25

Name of square Sum

1 (1+2+3+6+7+8+11+12+13) = 63

2 (2+3+4+7+8+9+12+13+14) = 72

3 (3+4+5+8+9+10+13+14+15) = 81

6 (6+7+8+11+12+13+16+17+18) = 108

7 (7+8+9+12+13+14+17+18+19) = 117

8 (8+9+10+13+14+15+18+19+20) = 126

The formula for the 2 x 2 square

Step size

4n + ? = 36

4 x 6 = 24 + ? = 36

? = 12

To prove that the formula is correct I will do the next two squares in the sequence numbers 8 and 9.

Square name 8

4 x 8 = 32

32 + 12 = 44

Square name 9

4 x 9 = 36

36 + 12 = 48

I am now going to do a 3 x 3 square inside a 5 x 5 square and get the formula.

1 2 3 4 5

6 7 8 9 10

1 12 13 14 15

6 17 18 19 20

21 22 23 24 25

1 2 3 4 5

6 7 8 9 10

1 12 13 14 15

6 17 18 19 20

21 22 23 24 25