This is reasonably fast. It pre-generates the whole list of candidates, so it's surely not the best. The optimization of making 5 and even numbers mutually exclusive makes a huge difference.
sub perms {
return () unless @_;
my ($car, @cdr) = @_;
# All permutations that do not include car
my @cdr_perm = perms(@cdr);
# All permutations that include car
my @car_perm = map {
my $this_perm = $_;
map {
substr($this_perm, 0, $_) . $car . substr($this_perm, $_)
} 0..length($this_perm)
} (@cdr_perm);
(@car_perm, @cdr_perm, $car);
}
my $max = 0;
OUTER:
for my $num (perms(reverse(1..4,6..9)), perms(9,7,5,3,1)) {
next unless $num > $max;
my @digits = split //, $num;
$num % $_ > 0 and next OUTER for @digits;
print "$num is divisible by all of @digits\n";
$max = $num;
}
print "Biggest found is $max\n";
Caution: Contents may have been coded under pressure.