How does Odysseus prove identity to Penelope?

First, Odysseus told Penelope that he is Odysseus. But Penelope wanted to make sure that it was the real Odysseus and not one of the suitors. So she gave him a challenge. ANd the challenge is: in their master bedroom...there was a bed and all 4 of the legs of the bed looked like a tree stump. And only 1 of the legs were a real tree. ANd only Odysseus and Penelope knew that. SO odyseus answered by saying pretty much that you are crazy and I can move that. SO therefore i is the real Odysseus!!!!