What kind of surreal contest is that?

Anyway, a rather quick solution would be to sort, and then look through the array, checking if the current element is identical to the previous or next. If no, it's unique.

Update: now with code:

# intentionally no warnings used.
my @array = qw(1 3 4 55 4 3 4 22 1 3 4 3 2 2 3 34);
@array = sort @array;

my $prev;
for (0..$#array) {
    my $i = $array[$_];
    print "$i\n" if $i != $prev && $i != $array[$_+1];
    $prev = $i;
}
[download]

Second update: Another idea. This one is O(n^2) in theory, but the regex engine being fast makes up for that in practise for low-ish values of n:

my @array = qw(1 3 4 55 4 3 4 22 1 3 4 3 2 2 3 34);
my $template = join ' ', @array;
study $template;

for (@array) {
    my @matches = ($template =~ /\b$_\b/g);
    print "$_\n" if 1 == @matches;

}
[download]