my $first = "the";
my $last = "dog";
my $string = "The black dog danced around the sleeping dog."
my @matches = $string =~ m/\b($first\b(?!.*?$first.*?)\b$last)\b/g;

##</code><code>##

my $first = "the";
my $last = "dog";

my @strings = ("The black dog danced around the sleeping dog.",
               "The brown bear leaped over the lazy dog.");

for my $string (@strings) {
    my @match = $string =~ m/(?=\b($first\b.*?\b$last)\b)/gi;

    for my $match (@match) {
        my @firsts = $match =~ m/\b($first)\b/gi;
        my @lasts = $match =~ m/\b($last)\b/gi;
        if ((@firsts == 1) and (@lasts == 1)) {
            print "$match\n";
        }
    }
}

# The black dog
# the sleeping dog
# the lazy dog