Ok, I ran out of time working on the "brute force" checking, but here is the shell of a program which should reduce the number of numbers which need to be checked to a small enough set. Sorry I could not complete the program (as it was actually starting to be fun. *Smiles*)

#!/usr/bin/perl
use strict;
use warnings;

use constant MATRIX_DIM => 3; # Set your matrix size here
use constant MAX_NUM    => (10 ** MATRIX_DIM) - 1;

# Since you need to find 2 times the matrix width distinct numbers, yo
+u cannot
# have a divisor greater than the maximum number divided by that produ
+ct.
# 
# For example, a 3 x 3 matrix has a maximum number of 999. You need 6 
+distinct 
# numbers to "solve" the matrix, so the maximum possible divisor would
+ be 166.
# 166 would result in 166, 332, 498, 664, 830, and 996.
#
my $Divisor = int(MAX_NUM / (MATRIX_DIM * 2)); 

my @Num;
my @Sol=();

sub CheckSolution
{
  my $pNum=shift;

  my @Sol=();

  # INCOMPLETE CODE
  #
  # Place code here which checks every combination of MATRIX_DIM numbe
+rs as rows
  # and sees if there are MATRIX_DIM other numbers which can act as co
+lumns.
  #
  # For example, for a 3 x 3 matrix, this code should go through each 
+combination
  # of three number (for rows) from the passed array and see if there 
+are three 
  # other numbers which would work with the selected rows as columns. 
+This should
  # be a workable computation for all smaller matrix sizes.
  #

  return @Sol;
}


while ($Divisor >= 1)
{
  @Num=();
  foreach (1..int(MAX_NUM / $Divisor))
  {
    next if (($Divisor * $_) < (MAX_NUM / 10)); #Skip numbers which be
+gin with zero
    push @Num, ($Divisor * $_);
  }
  print 'Checking solution for divisor ',$Divisor,': ',join('-',@Num),
+"\n";

  @Sol=CheckSolution(\@Num);
  last if ($#Sol > -1);
  $Divisor--;
}

print "\n";
if ($#Sol > -1)
{
  print 'Maximum divisor is ',$Divisor,', solution is ',join('-',@Sol)
+,"\n";
}
else
{
  print 'No solution found...',"\n";
}
[download]

Update: I finished code which will work on any size matrix and posted it Here.

Please note: I use "work" in the loosest terms as solving the 4x4 took 1.5 hours on my notebook.

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