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| '''Conway's LUX method for magic squares''' is an [[algorithm]] by [[John Horton Conway]] for creating [[magic square]]s of order 4''n''+2, where ''n'' is a [[natural number]]. | | Hello! <br>I'm Vietnamese male :). <br>I really like Rock stacking!<br><br>Feel free to visit my web page ... [http://orichinese.com/groups/hostgator-e-domini-it/ Hostgator Coupon] |
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| ==Method==
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| Start by creating a (2''n''+1)-by-(2''n''+1) square array consisting of
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| * ''n''+1 rows of '''L'''s,
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| * 1 row of '''U'''s, and
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| * ''n''-1 rows of '''X'''s,
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| and then exchange the '''U''' in the middle with the '''L''' above it.
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| Each letter represents a 2x2 block of numbers in the finished square.
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| 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:
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| :<math>\mathrm{L}: \quad \begin{smallmatrix}4&&1\\&\swarrow&\\2&\rightarrow&3\end{smallmatrix} \qquad \mathrm{U}: \quad \begin{smallmatrix}1&&4\\\downarrow&&\uparrow\\2&\rightarrow&3\end{smallmatrix} \qquad \mathrm{X}:\quad \begin{smallmatrix}1&&4\\&\searrow\!\!\!\!\!\!\nearrow&\\3&&2\end{smallmatrix}</math>
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| ==Example==
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| Let ''n'' = 2, so that the array is 5x5 and the final square is 10x10.
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| :{| class="wikitable" style="text-align: center" | |
| |L||L||L||L||L
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| |-
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| |L||L||L||L||L
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| |-
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| |L||L||U||L||L
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| |-
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| |U||U||L||U||U
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| |-
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| |X||X||X||X||X
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| |}
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| 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.
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| :{| class="wikitable" style="text-align: center"
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| | width="10%" | 68
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| | width="10%" | 65
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| | width="10%" | 96
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| | width="10%" | 93
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| | width="10%" | 4
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| | width="10%" | 1
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| | width="10%" | 32
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| | width="10%" | 29
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| | width="10%" | 60
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| | width="10%" | 57
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| |-
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| | 66 || 67 || 94 || 95 || 2 || 3 || 30 || 31 || 58 || 59
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| |-
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| | 92 || 89 || 20 || 17 || 28 || 25 || 56 || 53 || 64 || 61
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| |-
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| | 90 || 91 || 18 || 19 || 26 || 27 || 54 || 55 || 62 || 63
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| |-
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| | 16 || 13 || 24 || 21 || 49 || 52 || 80 || 77 || 88 || 85
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| |-
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| | 14 || 15 || 22 || 23 || 50 || 51 || 78 || 79 || 86 || 87
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| |-
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| | 37 || 40 || 45 || 48 || 76 || 73 || 81 || 84 || 9 || 12
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| |-
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| | 38 || 39 || 46 || 47 || 74 || 75 || 82 || 83 || 10 || 11
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| |-
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| | 41 || 44 || 69 || 72 || 97 ||100 || 5 || 8 || 33 || 36
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| |-
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| | 43 || 42 || 71 || 70 || 99 || 98 || 7 || 6 || 35 || 34
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| |}
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| ==See also==
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| *[[Siamese method]]
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| *[[Strachey method for magic squares]]
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| [[Category:Magic squares]]
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| {{numtheory-stub}}
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Hello!
I'm Vietnamese male :).
I really like Rock stacking!
Feel free to visit my web page ... Hostgator Coupon