is there a logical pattern when solving a 3x3 magic square that sums to 30?

Question

will the logical pattern work if the sum is a different number?

Answer 1

There are a couple of issues to address here. First, in a normal magic square, that is, a magic square that uses consecutive integers starting from 1, the sum of each column/diagonal/row must be fifteen. In order to sum to 30, you will need to take your "normal"solution and multiply each number by two.



Second, there are lots of patterns for producing magic squares.

For a 3x3, the one I remember from school is to put "1" in the middle of the top row. And then each number is added by moving diagonally up and to the right; if this move causes the number to leave the square, you put the number in either the bottom row or left column. If the move puts you in conflict with an already occupied space, then put the number directly below your current number.

So, if you start with 1 in the top center, the number two goes in the lower right (since the diagonal move puts it out of the square). 3 goes in the middle row first column; 4 would encounter 1, so put in under 3. Five goes in the middle of the square, 6 is in the upper right...follow this pattern to get:

8 1 6
3 5 7
4 9 2

for this to sum to 30, just mult by two:

16 2 12
6 10 14
8 18 4

I know my explanation of how to construct this is a little tortured; see the description at:

http://en.wikipedia.org/wiki/Magic_square#The_construction_of_a_magic_square_using_genetic_algorithms

and look for the section on a method for constructing a magic square of odd order"

have fun, these are really interesting mathematical structures

Answer 2

Magic Square Solver 3x3

Answer 3

You could, for example, start with a 3x3 magic square that has the numbers 1 through 9 and sums of 15. Then just add 5 to each individual value in the square so that the sum comes out to 30 instead of 15.

Answer 4

3x3 Magic Square Solver

Answer 5

logical pattern solving 3x3 magic square sums 30

Answer 6

Here is a magic square who sums all are 0. Any sum can be created.

a b c = 1 -4 3
d e f = 2 0 -2
g h i = -3 4 -1

Simply add 10 to each number!

Good luck.

Answer 7

Starting from the basic 'magic square'

618
753
294

You can apply any function to the numbers to generate a new sum - so to get from 15 --> 30 you can either double all the numbers or add 5 to all the numbers. If you wanted to get a number of (say) 24 you can either add 3 to all the numbers i.e. add 9 or multiply each by 1.6 (24/15)

Answer 8

2*magic(3)