Conway's 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 4n+2, where n is a natural number.

Method

Start by creating a (2n+1)-by-(2n+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:

Example

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

LLLLL
LLLLL
LLULL
UULUU
XXXXX

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.

68 65 96 93 4 1 32 29 60 57
666794952330315859
92892017282556536461
90911819262754556263
16132421495280778885
14152223505178798687
3740454876738184912
38394647747582831011
4144697297100583336
434271709998763534

See also

References

  • Erickson, Martin (2009), Aha! Solutions, MAA Spectrum, Mathematical Association of America, p. 98, ISBN 9780883858295.
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