In The Odyssey by Homer, although Odysseus is strong, he overcomes more obstacles with cunning than strength. What are some examples?
Another powerful example of Odysseus's cunning is his outwitting of the suitors who have invaded his home and pestered his wife and plotted to kill his son. Odysseus decides to enter his home at first disguised as a beggar in order to scope out the territory. While there, he is abused by the suitors, who insult him and, in the worst case, throw a stool at him. This section of The Odyssey is important because of the Greek rule of hospitality, which basically says that when a stranger asks for food or shelter in your home, you should treat him respectfully, feed him, clothe him, and do him no harm. One rather amusing portion of this rule is that you are to do all of this before asking who he is or what his business is in coming to you. In fact, in the strictest interpretations of this rule, you would feed and honor the guest for ten days before getting down to asking such questions. A fabulous example of this can be found in the myth of Bellerophon, who was sent to deliver a letter to a King--and the letter asked the King to kill Bellerophon! Well, his host treated Bellerophon like an honored guest for ten days before even reading the letter, and by that time, killing him was out of the question. The rule has its roots in the myth of Baucis and Philamon. Zeus and Hermes visit a town disguised as beggars and ask for food at each home, only to be turned away and taunted. Only Baucis and Philamon treat them to what little they have and are rewarded, while the rest of the town is destroyed. This myth led to the saying, "The stranger is sacred to Zeus." In fact, one of the suitors is so upset when a stool is thrown at the disguised Odysseus that he says this to the assailant.
Another example of this tradition is the way Odysseus is taken in and treated honorably by the Phaeacians when he lands upon their shores after Poseidon destroys his raft. It is only after several days of feasting him and even holding a festival in his honor that the king finally asks who he is. But the point is that if a stranger, a beggar, had come to Odysseus's palace when he was ruling it before he went to war, that stranger would have received royal treatment. So the contrast of the way the suitors treat Odysseus and the way he would have acted in their place cements the theme that these men are no good and deserve the death that awaits them.
Odysseus's cunning is on display again in the means he finds to kill the suitors, who outnumber him and his allies by about 120 to 4. He convinces Penelope to tell the suitors that she will agree to marry whichever of them can duplicate an old trick of Odysseus's--shooting an arrow through the handles of twelve axes spaced widely apart, using Odysseus's own old hunting bow. All the suitors try and fail, except for one or two who are afraid (after seeing everyone fail) to be embarrassed and attempt to delay the rest of the contest until the next day. However, Odysseus, still in his disguise, asks if he can try his hand at the shot. The suitors try to prevent this, again afraid to be shown up, particularly by a beggar, but in the end he is allowed to try the shot, which he easily executes. And then, with bow in hand, he begins to execute the suitors!
Greeks would have also been familiar with the cunning of Odysseus from legends about him that are not included in The Odyssey. It was Odysseus who came up with the idea of getting into the city of Troy by hiding a small group of warriors inside the Trojan Horse and then leaving the horse on the beach of Troy while the rest of the Greek fleet seemingly sailed away. The Trojans foolishly brought the giant horse into their city and in the middle of the night the warriors emerged, opened the city gates to the Greek army (which had quietly returned) and conquered the city. This is the origin of the saying, "Beware of Greeks bearing gifts," which implies that the "gift" was the Trojan Horse. In any case, in literature and mythology, Odysseus is the hero who best exemplifies cunning.
In The Odyssey by Homer, Odysseus solves many problems by cleverness. It is no coincidence that Athena, the goddess of wisdom, is the goddess that looks over him and aids him. In almost every episode, there is some example of a sneaky solution to a problem rather than use of brute force.
In the case of the Cyclops, who is far stronger than Odysseus, our hero triumphs first by getting Polyphemus drunk, and then blinding him using a burning, sharpened log. When Polyphemus traps Odysseus in the cave, he devises the plan of sneaking out clinging to the bellies of the rams.
Odysseus escaped the Siren's song by fashioning wax earplugs for his sailors but tying himself to a mast so that he could hear the song and not be seduced by it.
In The Odyssey, Odysseus also shows cunning by sending 2 of his men and a runner to check out the Land of the Lotus Eaters. Instead of blindly unloading the ship, Odysseus sends his men to scout to find out who lives on the land and determine if they are friend or foe.