"I know how to use the open function, but don't know how I would use it here."

Clearly you don't because you still maing the same mistakes. You aren't checking for errors opening files, I've mentioned this three times already:

The open documentation explains the difference between opening for writing and appending. You also shouldn't be opening the file for each print. See also How come when I open a file read-write it wipes it out? from perlfaq5. A short example:

#!/usr/bin/perl
use strict;
use warnings;

my @input = qw( a b c d );

open(my $fh, '>', "output.txt") or die "cannot open input file $!";

foreach(@input){
    print $fh "$_ \n";
}

close($fh);
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