my $calls = 0;
my $count = 0;
my @digits;
my @solutions;

append_digit();

print "count: $count\n", join("\n", @solutions), "\n";
print "recursive calls: ", $calls, "\n";

sub append_digit
{
    ++$calls;
    my $number = join '', @digits;

    if (@digits && ! grep { $number % $_ } @digits)
    {
        print "$count: $number\n" unless ++$count % 100;
        push @solutions, $number;
    }

    for my $digit (1 .. 9)
    {
        next if $digit ~~ @digits;

        push @digits, $digit;
        append_digit();
        pop  @digits;
    }
}