What does Penelope ask Odysseus, the beggar in disguise?
After being away at Troy for ten years and then another ten years wandering the seas in an effort to get back home, Odysseus returns to his native land of Ithaca. Unfortunately, when he returns home he hears that their are numerous suitors (108, to be precise) who are trying to convince his wife Penelope to marry one of them. They all assume Odysseus is dead.
Given the numerous suitors, Odysseus just can't walk right into his house and say, "Honey, I'm home." Thus, Odysseus disguises himself as a beggar and infiltrates his own home.
In Odyssey 19, the disguised Odysseus encounters his wife Penelope, who asks him several questions. First, Penelope says:
"Who are you, and where do you come from? What is your city, and who are your parents?" (A.S. Kline translation).
At first, Odysseus tries to dodge these questions, saying that it is too painful for him to think about these things. Eventually, though, he tells Penelope a false tale about how he had sailed from Crete and fought at Troy. He indicates that he knew Odysseus.
Penelope then tests him to find out whether he had really encountered her Odysseus:
"Now Stranger, I am forced to test you, and find out if you really entertained my husband and his godlike friends in your house, as you say. So describe what he was wearing, and what sort of man he seemed, and tell me about the comrades who were with him." (A.S. Kline translation)
Odysseus goes on to describe in great detail the clothes that Odysseus was wearing, as well as Odysseus' comrade Eurybates. As Penelope listens to the description, she realizes "the beggar" is telling the truth. Odysseus tries to ease her sorrow by predicting that Odysseus will return home.