The program I think you are asking for:

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

use constant UPPER_LIMIT => 6;

my ( @numbers, $count );
while ( @numbers < UPPER_LIMIT ) {
    my $guess = int 1 + rand UPPER_LIMIT;
    push @numbers, $guess unless grep $_ == $guess, @numbers;
    ++$count;
    }                       

print                       
    map( "$_\n", @numbers ),
    "How many times to get to ", UPPER_LIMIT, " is $count\n";

__END__
[download]

How the program should really be written:

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

use List::Util qw/ shuffle /;

use constant UPPER_LIMIT => 6;

my @numbers = shuffle 1 .. UPPER_LIMIT;

print
    map( "$_\n", @numbers ),
    "How many times to get to ", UPPER_LIMIT, " always ONE\n";

__END__
[download]