I don't think he was intending to load the entire file into memory. The trick is to keep an array of open FILEHANDLES and read one line at a time from each...

#!/usr/bin/perl -w
use strict;
use IO::File;

#interleave files, first argument is line count, rest are files.

my $lc = shift;
my @fhs;

foreach (@ARGV) {
  my $fh = new IO::File;
  open ($fh, "<$_");
  push @fhs, $fh;
}

while (--$lc) {
  foreach (@fhs) {
    print scalar(<$_>);
  }
}
[download]

Tested minimally but the path is clear from here I hope.

--
$you = new YOU;
honk() if $you->love(perl)