Here is what I think you are trying to do (Test data added, but code is untested).

use strict;
use warnings;
use Algorithm::Permute;

my @prdct = 55..66;
my @prdct1 = 'a'..'f';

my $product  = Algorithm::Permute->new( \@prdct );
my $product1 = Algorithm::Permute->new( \@prdct1 );


while ( my @res = $product->next ) {
  chomp @res;
  my $chk = join " + ", @res;
  print "chk:$chk\n";
  $product1->reset; # Allow to iterate again
  while (my @res1 = $product1->next ) {
      chomp @res1;
      my $chk1 = join( ' + ', @res1); 

      print "\tchk1:$chk1\n";
      my  $chk3 = "$chk <=> $chk1";
      my  $chk4 = "$chk1 <=> $chk";
  }
}
[download]