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With a brute force program solver written in C#, I found a solution with sum 366:

    3 11  5 | 19
   37 17 13 | 67
    7 31 23 | 61
   ---------+---
29 47 59 41 | 43

The program still runs, though, so there might be better solutions.

Source code at PasteBin (you might want to change the initial value of recordSum to something bigger than 366 to actually get some results).

With a brute force program solver written in C#, I found a solution with sum 366:

    3 11  5 | 19
   37 17 13 | 67
    7 31 23 | 61
   ---------+---
29 47 59 41 | 43

I let the program run until the top left corner was 61, so I'm pretty sure that there are no better solutions, but feel free to look for yourself:

Source code at PasteBin (you might want to change the initial value of recordSum to something bigger than 366 to actually get some results).

With a brute force program solver written in C#, I found a solution with sum 366:

    3 11  5 | 19
   37 17 13 | 67
    7 31 23 | 61
   ---------+---
29 47 59 41 | 43

The program still runs, though, so there might be better solutions.

With a brute force program solver written in C#, I found a solution with sum 366:

    3 11  5 | 19
   37 17 13 | 67
    7 31 23 | 61
   ---------+---
29 47 59 41 | 43

The program still runs, though, so there might be better solutions.

Source code at PasteBin (you might want to change the initial value of recordSum to something bigger than 366 to actually get some results).

With a brute force program solver written in C#, I found a solution with sum 396:

    3  5 11 | 19
   13 17 37 | 67
   31  7 23 | 61
   ---------+---
59 47 29 71 | 43

The program still runs, though, so there might be better solutions.

With a brute force program solver written in C#, I found a solution with sum 366:

    3 11  5 | 19
   37 17 13 | 67
    7 31 23 | 61
   ---------+---
29 47 59 41 | 43

The program still runs, though, so there might be better solutions.