use strict;
use warnings;

my @numbers = qw( 113443 143132 241131 321422 323132 331222
				  341114 412433 414422 431331 443112 444313 );
				
# find possible positions
my %positions;
for my $n (@numbers) {
	$positions{$n} = [];
	# frequency of digits in current number
	my @nfreq = (0) x 5;
	$nfreq[$_]++ for split //, $n;
	# check which position is possible
	for my $p (0..5) {
		# frequency of digits in current position w/o current number
		my @freq = (0) x 5;
		$freq[substr( $_, $p, 1 )]++ for @numbers;
		$freq[substr( $n, $p, 1 )]--;
		# check if position is feasible
		# ie enough of each digit available
		my $possible = 1;
		$freq[$_]<$nfreq[$_] and $possible = 0 for 1..4;
		push @{$positions{$n}}, $p if $possible;
	}
}

for my $n (sort { scalar(@{$positions{$a}}) <=> scalar(@{$positions{$b}}) } @numbers) {
	print "Number $n can be at positions @{$positions{$n}}.\n";
}