#!/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, you cannot
# have a divisor greater than the maximum number divided by that product.
# 
# 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 numbers as rows
  # and sees if there are MATRIX_DIM other numbers which can act as columns.
  #
  # 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 * $_) < (MAX_NUM / 10)); #Skip numbers which begin with zero
    push @Num, ($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";
}