not quite sure i understand the problem, but here's one Mathematica approach:

  m = {{39, 90, 75, 88, 15, 57},
     {9, 2, 58, 68, 48, 64},
     {29, 55, 16, 67, 8, 91},
     {40, 54, 66, 22, 32, 25},
     {49, 1, 17, 41, 14, 30},
     {44, 63, 10, 83, 46, 3}};

  Select[
   Extract[m, #] & /@ Transpose[{Range[6], #}] & /@ Tuples[Range[6], 6],
   Total[#] == 419 &]