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# Parent
sub get_child_id {
...
  # Find the index of the child. Left as exercise for the reader (read
+: I'm too lazy :) ).
  return $child_index;
}

# Child
sub whereami {
...
  my $id=$parent->get_child_id($self);

}

my $self = {
      parent => \$parent;
   };

my $self= { parent => $parent }; #$parent is a ref, you were storing a
+ ref to $parent