Montresor is the protagonist and narrator of "The Cask of Amontillado" by Edgar Allan Poe, and he is clearly not sane. Despite that fact, he is quite clever. He feels he has been somehow injured by a fellow wine connoisseur named Fortunato, and Montresor determines that he has been pushed too far and must now take his revenge on his colleague Fortunato.
Two things are crucial to Montresor's plan working, and both of them involve his use of psychology to make things happen. The first is that no one at all must be in his house so he can dispose of Fortunato as he wishes without fear of discovery. It is Carnival time, and of course Montresor is perfectly bright enough to know that all of his servants would rather be out celebrating than doing their jobs on his estate. Montresor makes a brilliant move:
There were no attendants at home; they had absconded to make merry in honour of the time. I had told them that I should not return until the morning, and had given them explicit orders not to stir from the house. These orders were sufficient, I well knew, to insure their immediate disappearance, one and all, as soon as my back was turned.
This is a bold example of reverse psychology. Montresor does not say he even checked to see if they left; he simply knew they would all be gone. This is a great example of Montresor using psychological trickery, but it is also an indication that in some respects Montresor is capable of rational, even exceptional thinking.
The second thing that must happen if Montresor's plan is going to succeed is that he must find a way to lure the unsuspecting Fortunato not only back to his estate but into the crypts below the house. To do this, Montresor appeals to Fortunato's weakness--his pride.
He had a weak point --this Fortunato --although in other regards he was a man to be respected and even feared. He prided himself on his connoisseurship in wine. Few Italians have the true virtuoso spirit. For the most part their enthusiasm is adopted to suit the time and opportunity, to practise imposture upon the British and Austrian millionaires. In painting and gemmary, Fortunato, like his countrymen, was a quack, but in the matter of old wines he was sincere. In this respect I did not differ from him materially; --I was skilful in the Italian vintages myself, and bought largely whenever I could.
Because Fortunato is so certain he has the best wine palate in the city, Montresor simply lies and tells Fortunato that he has a cask of Amontillado, something Fortunato could not believe without tasting it. Every single time Montresor senses that Fortunato is wavering in his resolve to follow Montresor to the non-existent cask of wine, Montresor invokes the name of Luchresi, a man Fortunato claims "cannot distinguish Sherry from Amontillado."
This appeal to Fortunato's excessive pride does work (and is something that might have worked on Montresor, as well, as he is equally proud of his wine palate) and he follows Montresor all the way to his doom. One added strategy is that Montresor consistently gives wine as "medicine" to Fortunato for his cough, getting Fortunato drunk enough that he does not question Montresor's acts as much as he might.
This deliberate and rather intricate plan relies on Montresor's keen mind and knowledge of human nature, something quite confounding in a man who is obviously not sane.