What test does Penelope give Odysseus to determine if he is really Odysseus?
Penelope tells one of the maids to move the bed from the couple's bedroom for the "stranger" to sleep in. Only Odysseus, Penelope, and the maid know that the bed cannot be moved because Odysseus built it with an olive tree trunk as one of the bedsteads. Angrily, Odysseus demands to know how the bed can possibly be moved. With this question, Penelope knows this man truly is her husband who has finally returned. Her test shows she is a clever woman equal to Odysseus in cunning.
After twenty long years (ten of which Odysseus spent fighting in the Trojan War and another ten he spent wandering land and sea in search of home) of waiting for the homecoming of her husband, Odysseus, Penelope has remained a steadfast, dutiful, but incredibly discerning wife. Once believing her husband to be dead, she is hesitant to buy the story of the strange man in rags who has showed up on her doorstep, killed off all her other unwanted suitors, and proclaimed himself her true spouse.
Thus, Penelope devises a plan to test out the identity of this "stranger." Penelope asks her maid, Eurycleia, to bring the bed frame from the bedroom she and Odysseus once shared into the hall so that he may rest, knowing that only the real Odysseus would know that this act was impossible--Odysseus had constructed the frame so that it was attached to an olive tree within the room. Odysseus immediately reacts with great anger, stating:
But among me there is no one living,
no matter how much energy he has,
who would find it easy to shift that bed.
For built into the well-constricted bedstead
is a great symbol which I made myself
with no one else. A long-leaved olive bush
was growing in the yard...
I built my bedroom round this olive bush,
till I had finished it with well-set stones...
Odysseus goes on to explain how he built the bed, and Penelope reacts with utter joy, realizing that this man truly is her long-lost husband.
One of the masterful ways that Homer makes the story so compelling is by building up so much tension along the way to a resolution. Odysseus has finally returned home and the reader expects a tearful reunion with Penelope but she is absolutely steadfast in her unwillingness to trust that it is in fact her husband under the rags. Even when Odysseus is restored to his handsome and well-dressed self, Penelope still doesn't trust.
And so we come to the moment that Odysseus, out of frustration, demands that a bed be brought to the great hall so that he can rest. Penelope sees a moment to test the man who claims to be Odysseus by suggesting that their own bed be brought for him. Odysseus launches into an outraged tirade at the suggestion and describes exactly why the bed (built out of an olive tree with roots still planted firmly in the ground) cannot be brought out to him.
Only then does Penelope trust that this man is in fact Odysseus and embraces him tearfully.