http://www.perlmonks.org?node_id=266572

artist has asked for the wisdom of the Perl Monks concerning the following question:

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]
]
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 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]]
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;
}
}