Dear Monks

I found an interesting puzzle and here is my attempt to solve it. Let say we have NxN matrix.

[ 
  [1, 2]  
  [4, 8]
]
[download]

By Joining the columns and rows individually, I get the following four formed-numbers. 12,14,28,48 There Common Divisor is '2'. I like to find the matrix with the highest common divisor. Some condtions are..

• No formed-number should start with 0.
• No two formed-numbers be same.

I can do it easily for 2x2 matrix and found highest divisor as 7. and the formed-numbers : 28,21,14,84.

[[2,8]
 [1,4]]
[download]

How I can do with higher dimentions more efficiently? Even for 3X3 with it has to test around billion numbers with my method.

$| += 1;
foreach my $divider (2..9){
    print "Divider $divider\n";
  N: foreach $n (1111..9999){
      next if $n =~ /0\d+/;
      @n = split //,$n;
      my $count  = 0;
      my @pairs;
      my %pairs;
      foreach (qw(01 02 13 23)){
      my($p,$q) = split //;
      my $num = $n[$p].$n[$q];
      push @pairs, $num;
      next N if defined $pairs{$num};
      $pairs{$num} = 1;
      $count++ if $num % $divider  == 0;
      }
      print join " " => @pairs,"\n" if $count == 4;
  }
}
[download]

Thanks
artist

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