my @files = ("1.txt", "2.txt", "3.txt");
my @fhs;

foreach my $file (@files) {
     open($fh, $file) || die;
     push(@fhs, $fh);
}
open(MIXED, "mixed.txt") || die;
while (1) {
     foreach $fh (@fhs) {
         $line = <$fh>;
         last if (eof($fh));
         print MIXED $line;
     }
}
map { close($_); } @fhs;
close(MIXED);