It is easy to make a matrix of squares, being the same up as down and and odd number of rows and columns from 9 - 25 - 81 etc and have have equal amounts for each row and column. My question is simply - is there another formula for an even amount on boxes each way?

  • $\begingroup$ I recommend you to look at the top answer from this math.stackexchange question. $\endgroup$ – user40086 Sep 8 '17 at 11:21
  • $\begingroup$ Are you asking how to construct a magic square of even order? $\endgroup$ – MikeQ Sep 8 '17 at 11:40
  • $\begingroup$ Your wording is confusing, what do you mean by "being the same up as down"? Perhaps you could edit your question to include an example of a 5x5 square which fits your criteria. $\endgroup$ – Mike Earnest Sep 8 '17 at 15:51
  • $\begingroup$ Has a correct answer been given? If so, please don't forget to $\color{green}{\checkmark \small\text{Accept}}$ it :) $\endgroup$ – Rubio Sep 16 '17 at 14:13

This question has asked before on the math.stackexchange site, and I will summarise the answers there below.

The relevant portion:

A very elegant method for constructing magic squares of singly even order $n=4m+2$ with $m\geq1$ is due to J. H. Conway's 'LUX' method. Create an array consisting of $m+1$ rows of Ls, $1$ row of Us, and $m-1$ rows of Xs, all of length $n/2=2m+1$. Interchange the middle U with the L above it. Now generate the magic square of order $2m+1$ using the Siamese method centered on the array of letters (starting in the center square of the top row), but fill each set of four squares surrounding a letter sequentially according to the order prescribed by the letter. That order is illustrated on the left side of the bellow figure, and the completed square is illustrated to the right. The "shapes" of the letters L, U, and X naturally suggest the filling order, hence the name of the algorithm.

In case this is confusing, the diagram below should help.

LUX method illustrated

For further reading, you might want to look at this Wolfram MathWorld page which goes into more detail about the formation of magic squares.


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