Magic squares of odd order: Difference between revisions

=={{header|Mathematica}}==

Rotate rows and columns of the initial matrix with rows filled in order 1 2 3 .... N^2

Method from http://www.jsoftware.com/papers/eem/magicsq.htm

<lang Mathematica>

rp[v_, pos_] := RotateRight[v, (Length[v] + 1)/2 - pos];

rho[m_] := MapIndexed[rp, m];

magic[n_] :=

rho[Transpose[rho[Table[i*n + j, {i, 0, n - 1}, {j, 1, n}]]]];

square = magic[11] // Grid

Print["Magic number is ", Total[square[[1, 1]]]]

</lang>

Output (alignment lost in translation to text):

{68, 80, 92, 104, 116, 7, 19, 31, 43, 55, 56},

{81, 93, 105, 117, 8, 20, 32, 44, 45, 57, 69},

{94, 106, 118, 9, 21, 33, 34, 46, 58, 70, 82},

{107, 119, 10, 22, 23, 35, 47, 59, 71, 83, 95},

{120, 11, 12, 24, 36, 48, 60, 72, 84, 96, 108},

{1, 13, 25, 37, 49, 61, 73, 85, 97, 109, 121},

{14, 26, 38, 50, 62, 74, 86, 98, 110, 111, 2},

{27, 39, 51, 63, 75, 87, 99, 100, 112, 3, 15},

{40, 52, 64, 76, 88, 89, 101, 113, 4, 16, 28},

{53, 65, 77, 78, 90, 102, 114, 5, 17, 29, 41},

{66, 67, 79, 91, 103, 115, 6, 18, 30, 42, 54}

Magic number is 671

Output from code that checks the results

Rows

{671,671,671,671,671,671,671,671,671,671,671}

Columns

{671,671,671,671,671,671,671,671,671,671,671}

Diagonals

671

671