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

for ($i = 0; $i < scalar(@files); ++$i) {
     open($fhs[$i], $files[$i]) || die;
}
open(MIXED, ">mixed.txt") || die;
OUTER:
while (1) {
     foreach $fh (@fhs) {
         last OUTER if (eof($fh));
         $line = <$fh>;
         print MIXED $line;
     }
}
map { close($_); } @fhs;
close(MIXED);