LUX Method For Magic Squares

Conway's LUX method for magic squares is an algorithm by John Horton Conway for creating magic squares of order 4''n''+2, where ''n'' is a natural number.

Method

Start by creating a (2''n''+1)-by-(2''n''+1) square array consisting of
* ''n''+1 rows of Ls,
* 1 row of Us, and
* ''n''-1 rows of Xs,
and then exchange the U in the middle with the L above it.

Each letter represents a 2x2 block of numbers in the finished square.

Now replace each letter by four consecutive numbers, starting with 1, 2, 3, 4 in the centre square of the top row, and moving from block to block in the manner of the Siamese method: move up and right, wrapping around the edges, and move down whenever you are obstructed. Fill each 2x2 block according to the order prescribed by the letter:

:$\mathrm: \quad \begin4&&1\\&\swarrow&\\2&\rightarrow&3\end \qquad \mathrm: \quad \begin1&&4\\\downarrow&&\uparrow\\2&\rightarrow&3\end \qquad \mathrm:\quad \begin1&&4\\&\searrow\!\!\!\!\!\!\nearrow&\\3&&2\end$

Example

Let ''n'' = 2, so that the array is 5x5 and the final square is 10x10.
:

Start with the L in the middle of the top row, move to the 4th X in the bottom row, then to the U at the end of the 4th row, then the L at the beginning of the 3rd row, etc.

:

See also

* Siamese method
* Strachey method for magic squares

References

*{{citation, title=Aha! Solutions, series=MAA Spectrum, first=Martin, last=Erickson, publisher=Mathematical Association of America, year=2009, isbn=9780883858295, page=98, url=https://books.google.com/books?id=ywKyQz7_4-MC&pg=PA98.

Magic squares