Yay! I love that book and have read it a thousand times. I remember each part. Odysseus convinces Penelope that he is actually Odysseus by stringing a bow, and then shooting an arrow through 12 ax heads. Penelope knew it was Odysseus because no other man was able to get past these challenges. After he completes these challenges, he tells Penelope something that nobody but the Gods know. He told Penelope about the bed he crafted just for her. I hope this helps! It is a really good book isn't it? : )
