Here's a simple one, that seems to cover it:

The "data" is a file called "lines":

1 flew over the cuckoos nest
12 flew over the cuckoos nest

#!/usr/bin/perl -w

use strict;

my $line = "/home/trix/lines";

open (L, "$line") || die "$!\n";
while (my $lines = <L>) {
  chomp $lines;
  if ($lines =~ /^1{1}\D/) {
    print "my lines are $lines\n";
  }
  else { print "Nope!\n";
       }
}
[download]

Update: this regex doesn't catch lines that begin with "1d", for instance. Take other's suggestions.