4x4 Magic Square.

Forum|Forum|10 years ago
January 17, 2016
2 replies
4011 views

Hello, Everyone.

(1).PNG

Is it possible to solve M matrix, the above ?

Thanks in advance for your time and help.

Regards.

1_4-x-4-Magic-Square-xmcd.zip

Algebra_Geometry

Best answer by LucMeekes

One can get quite far though:

It's just that the inequality constraint (involving M01 and M03) is not obeyed. Note that I first tried:

But then I got an error message saying it's not allowed inside a solve block.

Luc

L

LucMeekes

23-Emerald IV

At first glance: no

Reason: your system is over-constrained. You have 16 variables to find, you can have only 16 constraints.

The requirement of a magic square (sums of all 4 rows and of all 4 columns and along the 2 main diagonals must be equal) already gives you at least 4+4+2-1=9 constraints. Now you've added 16 more constraints, totalling 25.

Another constraint from the magic square is that all your variables must be different AND in the range 1 through 16.

Success!

Luc

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-MFra-

21-Topaz II

Dürer matrix.jpg

W

Werner_E

25-Diamond I

Apart from what Luc already wrote you would have to constraint the matrix elements to be integers - something which Mathcad is not really good at.

So I guess the better option to get a magic square is to write a program following one of the algorithms to build a magic square. There a quite some in print, ususally differing according to the magnitude of the sqare, distinguishing odd or even order and as far as I remember ther is a short algorithm dealing with squares of a mgnitude which is divisable by 4.

What exactly ist the problem you should solve for homework?

WE