I'd read before that the riddle does not appear in Elegant Extracts, despite what Emma says. So why did JA put this erroneous factual statement in Emma's mouth? I can't see that we're meant to see Emma as a liar, which isn't in her character. And would the reader be expected to know the riddle was not in Elegant Extracts?

Maybe the point was to cover up Emma's seeming indelicacy by giving her a justification for putting the riddle in Harriet's book? That is, JA was making it seem as if there's nothing wrong with the riddle by saying it was printed in Elegant Extracts?

The more I think of this, I think it was JA making sly fun of her characters -- and readers. I think she was feeling sick and wicked. And she had Emma state (falsely) that the riddle was in Elegant Extracts to bury the joke a little more so people wouldn't notice. Maybe also a poke at the Extracts themselves?