Why woldn't you just do something like the following (untested, sorry):

#!perl
use strict;
use warnings;

my @handles;
my $i = 0;
for (@ARGV) {
   open $handles[$i++], '<', $_
      or die "Failed to open $_: $!\n";
}

my $line;
$i = 0;
while (1) {
   $line = <$handles[$i]>;
   defined($line) or last;
   print $line;
} continue {
   ++$i;
   $i %= @handles;
}

close $_ for @handles;
[download]

Hope this helped.
CombatSquirrel.

Update: Closed files. Thanks to b10m.

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Entropy is the tendency of everything going to hell.