You are definately overusing <INPUT>. Each time you do that, it reads another line... Your loop only checks every 3rd line for /^Algorithm/. It chomps the first line, checks the second one for /^Experiment Name/, and checks the third for /^Algorithm/.

I'd write that subroutine as:

sub getExpNumber {
  my $filePath = shift;
  my $n;

  open (INPUT,"<$filePath") or die "Can't open $filePath: $!\n";
  while (<INPUT>) {
    chomp;
    last if /^Experiment Name/;
    $n++ if /^Algorithm/
  }
  print "There are $n experiments in $filePath\n"
  close(INPUT) or die "Can't close $filePath: $!\n";
  return $n;
}
[download]

/pattern/ works on $_ if nothing is bound to it, and while(<FILE>) {...} puts the line read into $_. So the two statements that have if /pattern/ at the end match the line read.