Here is my code guys. I strongly favour non-recursive solutions given the long time it's taking to generate all the possible combinations.

my $limit = 9;
my @empty_array = ();
generate_all_combinations_of_free_variables($limit, \@empty_array);

sub generate_all_combinations_of_free_variables{
    
    my $limit = shift;
    my $current_array = shift;
    my %combinations=();
    
    
    if (@$current_array == $limit){
        my $str = join("", @$current_array);
        $combinations{$str}++;
        return \%combinations;
    }
    
    if(@$current_array != $limit){
        my @new_array = @$current_array;
        push @new_array, 0;
        my $combin1 = generate_all_combinations_of_free_variables($lim
+it, \@new_array);
        
        @new_array = @$current_array;
        push @new_array, 1;
        my $combin2 = generate_all_combinations_of_free_variables($lim
+it, \@new_array);
        
        my %combined_hash = (%$combin1, %$combin2);
        
        return \%combined_hash;
    }
}
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