What is the question that Cyclops asks Odysseus that "put him [Odysseus] to the test" in Homer's "Odyssey"?
The question that Cyclops asks Odysseus specifically to "put him to the test" is "tell me where you made your ship fast when you came on shore". Odysseus has said that he is a visitor from afar and as such is entitled to hospitality and a gift. Cyclops, scornful that Odysseus does not know that Cyclops' people follow no laws and therefore care nothing about how they treat their guests, hopes to "trip him up" further and asks, if his explanation of where he is from is true, then where is his boat - "is it round the point, or is she lying straight off the land?" Odysseus, realizing that "(Cyclops) said this to draw (him) out" was "too cunning to be caught in that way" and so answers with a lie, telling Cyclops that his ship has been wrecked, and that he and those who had come ashore with him are the only survivors.
(Quotes are form the translation of Book IX of Homer's "Odyssey" referenced at the first link below)
The question the cyclops asks of Odysseus is "what is your name?" Odysseus answers "no man", and when Odysseus' men blind Polyphemus (the cyclops) with a burning stake, he cries for help, saying that "no man" attacked him. Polyphemus' allies interpret his injury as a curse from the the Gods, which, ironically, is the effect Odysseus' actions have on his crew, as Poseidon, Polyphemus' father, curses Odysseus.