Penelope's choice of contest — one that only Odysseus could win — supports the suspicion that she is aware of the beggar/Odysseus's real identity. When the beggar/Odysseus asks for an unofficial chance at the bow, Penelope immediately counters Antinous' objection. Dismissing the idea that the guest would claim her as his bride, she responds that by giving the wandering stranger a shot she is simply being hospitable. Of course, the beggar would not claim her for his bride; Odysseus would not have to.
