• it works only if n is odd.
• Place a 1 in the middle of the bottom row.
• After k has been placed in the (i, j) square, place k+1 into the square to the right and down, wrapping around the borders.
• However,
  1. if the square to the right and down has already been filled, or
  2. if you are in the lower right corner,
  then you must move to the square straight up instead.

Here's the 5-by-5 square that you get if you follow this method:

 11  18   25    2    9 
 10  12   19   21    3 
  4   6   13   20   22 
 23   5    7   14   16 
 17  24    1    8   15 

Calculate the 3-by-3, 7-by-7 and 13-by-13 magic squares.

Here's how my code is working:

-bash-3.1$ java Magic 3
  4   9   2 
  3   5   7 
  8   1   6 
-bash-3.1$ java Magic 5
 11  18  25   2   9 
 10  12  19  21   3 
  4   6  13  20  22 
 23   5   7  14  16 
 17  24   1   8  15 
-bash-3.1$ java Magic 7
 22  31  40  49   2  11  20 
 21  23  32  41  43   3  12 
 13  15  24  33  42  44   4 
  5  14  16  25  34  36  45 
 46   6   8  17  26  35  37 
 38  47   7   9  18  27  29 
 30  39  48   1  10  19  28 
-bash-3.1$ java Magic 9
 37  48  59  70  81   2  13  24  35 
 36  38  49  60  71  73   3  14  25 
 26  28  39  50  61  72  74   4  15 
 16  27  29  40  51  62  64  75   5 
  6  17  19  30  41  52  63  65  76 
 77   7  18  20  31  42  53  55  66 
 67  78   8  10  21  32  43  54  56 
 57  68  79   9  11  22  33  44  46 
 47  58  69  80   1  12  23  34  45 
-bash-3.1$ java Magic 11
 56  69  82  95 108 121   2  15  28  41  54 
 55  57  70  83  96 109 111   3  16  29  42 
 43  45  58  71  84  97 110 112   4  17  30 
 31  44  46  59  72  85  98 100 113   5  18 
 19  32  34  47  60  73  86  99 101 114   6 
  7  20  33  35  48  61  74  87  89 102 115 
116   8  21  23  36  49  62  75  88  90 103 
104 117   9  22  24  37  50  63  76  78  91 
 92 105 118  10  12  25  38  51  64  77  79 
 80  93 106 119  11  13  26  39  52  65  67 
 68  81  94 107 120   1  14  27  40  53  66 
-bash-3.1$