Bat Deduction

"Batman: Pretty fishy what happened to me on that ladder. Gordon: You mean, where there's a fish, there could be a Penguin. Robin: But wait! It happened at sea! See? "C" for Catwoman! Batman: Yet -- that exploding shark was pulling my leg! Gordon: The Joker! O'Hara: It all adds up to a sinister riddle... Riddle-er. Riddler?"

- Batman: The Movie

So you have the average detective story, with a huge, widely spanning mystery that has both the detective and the viewers stumped. You've got it going, but, now that you're in the thicket, you've run yourself into a corner. It would take more space than available to connect the pieces, and you don't want to drag the viewer along with boring step by step exposition, so what are you going to do?

Wait, your main character is a detective, isn't he? Why not just have him deduce that these things are connected, and move on. He's a genius, why not just leave it at that?

In short, this is when a character makes a huge jump to reach a conclusion, often through a mental Wiki Walk, that has to be made in order for the plot to progress, but without any real explanation for what might have spurred the conclusion.

Often used in cases where the viewers already know that everything's connected and how they connect, but there's no in-story explanation, and the plot really needs to get to the next part.

Detective novelist Ronald A. Knox discouraged the use of this in his Decalogue for detective fiction.

The Trope Namer is Batman, specifically the 60's Adam West Batman, who, given his title as the World's Greatest Detective, can easily fall into this when a writer gets into a rut (or is playing it up for laughs). Can also be interpreted as "batshit crazy deduction," or, less often, "lazy writer deduction."

Compare Eureka Moment, where the seemingly illogical leap actually does have a logical explanation - it just doesn't get explained at the time in order to keep up the suspense; when the last clue is a Smoking Gun, making the previous ones redundant, it's Clue, Evidence, and a Smoking Gun; Conviction by Counterfactual Clue, where the logic is based on faulty deduction; and Right for the Wrong Reasons, where the logic is (usually) correct but the premises are mistaken. Also see Only the Author Can Save Them Now. This is a natural result of having Super Intelligence. May look a lot like Insane Troll Logic, except in this case the deduction is correct. Epileptic Trees are fan theories that look like this. Contrast with Clue, Evidence, and a Smoking Gun where no deduction is really needed.

Anime & Manga

 * This is a key feature of Case Closed, owing to difficulty translating. In the original Japanese version of Detective Conan, an unfortunately large number of clues rely on Japanese puns and cultural references that can't really be translated, so non-Japanese readers/viewers can't fit the clues together.
 * Though the case involving was easier to solve for Western audiences.
 * Death Note
 * Near does this, especially in the anime, which compressed a 5 volume arc into 11 episodes. The manga explains his deductions a lot better—with huge walls of text.
 * In early episodes of the anime, L does a bit of this but it drops off as enough clues are established for the audience to follow what's happening. The bilinear narration between Light and L only makes it all the more obvious.
 * This is how Lucy deducted where Mavis' grave was in the exam arc of Fairy Tail. We have six hours to find the grave? The only six letter word related to death is "demise"… and it is the only one that has the letter "E" twice… so the grave is somewhere in the E route of the first exam!
 * While the story does have elements of a Fair Play Whodunnit, the mysteries in Gosick are often solved by Victorique putting together wildly varying pieces of information, information provided secondhand more often than not, and using it to put together the elaborate scenarios that make up the mystery.

Comics -- Books

 * Justified in Grant Morrisons Batman, where Batman points out that he needs to use half-mad logic and bizarre connective leaps to "match wits" with a rotating group of homicidal, delusional sociopaths, or people will die. Likewise, the Joker himself admits that Batman may have driven him to apophenia, as he has to constantly wonder whether or not the Bat will solve anything he plans, no matter how random everything seems.
 * Taken still further during Morrison's Justice League run by Martian Manhunter who shapeshifts his brain to make the irrational intuitive regions big and the logical regions small so he can think like the Joker. The chaotic maze he and Superman are trapped in suddenly appears to have a straight path from entry to exit.
 * Parodied in Nemesis, where the title villain tries coming up with some riddles with which to taunt the police. "What's black and white and red all over?"

Fan Works
"Joseph: Nrg! I don't have time for this. Wait, Time. Chronos was the god of time in Greek mythology. Greece won the Euro cup in 2004. George Bush was re-elected in 2004. George Bush was impersonated in Harold and Kumar Escape From Guantanamo Bay. Kal Penn is a part of Barack Obama's administration. Will Smith looks like Barack Obama. Will Smith's son's going the be in the next Karate Kid... Oh my god I've got it!"
 * Parodied in JoJo's Bizarre Adventure Abridged, where Joseph, through an insane series of jumps ends up with a totally false deduction. Fortunately, Dio doesn't know he's barking up the wrong tree and ends up spilling the beans before Joseph can lay his bizarre theory on him.


 * The Darker Knight takes this to an extreme.

Films -- Live-Action

 * In Batman: The Movie, the entire universe runs on Bat-Logic, in the name of fun, though. For example, at the beginning Batman gets a series of "joking" riddles that vaguely talk about birds and the sea. Batman reasons out that the riddles must be from Riddler (fair enough), but the joking style is a sign he's working with the Joker (makes some sense) and the reference to birds is the Penguin (OK, I guess) and the reference to the sea... well, C as in Catwoman (...)! Meaning the four of them are working together. And Batman is absolutely right.
 * There is NO way the following exchange can be described as a logical conclusion to anything. "What weighs six ounces, sits in a tree and is very dangerous?", our heroes mull over this important clue. "A sparrow with a machine gun!" Robin deduces. This is, of course, the right answer.
 * Two riddles have the answers "egg" and "make applesauce". This means the villains are going to attack the Expy for the UN. You see, applesauce is a single unified mixture (like the UN), and the egg is a capsule (like the UN).
 * In Batman Forever, upon discovering that Edward Nygma was the one sending him creepy riddles anonymously (which to the untrained eye, probably looked stalkerish but harmless), Batman instantly deduced that Nygma had actually killed a co-worker who was thought to have committed suicide. With no evidence whatsoever.
 * Of course, this trope always comes into play when the Riddler is involved. However, the four riddles that eventually lead Batman to deduce the Riddler's identity are, on their own, perfectly reasonable: it's the clues hidden in the riddles that pretty much defy logic. To elaborate: Each riddle has a number in it: 13, 1, 8 and 5. These correspond to the letters M, A, H and E. Bruce puts 1 and 8 together, making it MRE. MRE = Mr. E = Mystery. Another word for Mystery is Enigma, leading him to conclude that the Riddler is Mister E. Nygma. At least in the Peter David novelization he had to spend some time after finding the numbers trying to work out the meaning.
 * The movie does show that Bruce Wayne is dubious about the supervisor's apparent suicide from day one, so much so that he ordered full benefits be paid out to the man's family even though their insurance doesn't cover suicide (he's versed in psychology and must have observed that the supervisor didn't seem suicidal). Put that together with the scene Bruce had witnessed earlier with the belligerent supervisor humiliating the clearly unstable Nygma and its not so big a leap for Bruce to conclude that Nygma murdered his boss once Bruce knew that Nygma was a supervillain.
 * For what it's worth, the riddles in the movie were devised by New York Times puzzlemaster Will Shortz.
 * In fact, one of the reasons the Riddler was never used that much in comics even before he reformed was that it's hard to get around this trope where he's concerned without making the riddles insultingly easy—you not only have to write a genius but you have to write a Batman capable of outthinking a genius.
 * In Evolution, the scientists reason that, since arsenic is poisonous to carbon-based life forms, the nitrogen-based aliens must be poisoned by selenium. How do they reach this deduction? Because arsenic is two spaces up and one space to the right on the periodic table, so this pattern should hold true for nitrogen.
 * In Superman, Lex Luthor somehow reasons that kryptonite is lethal to Superman just because he is from Krypton and that pieces of Krypton must have fallen to Earth just because of the location and time of Krypton's explosion in 1948 (which he knows from reading details in Superman's interview with Lois Lane, which Superman never actually provides in the interview scene—and according to the disembodied voice of Marlon Brando by the time the rocket ship carrying Superman reached Earth, thousands of Earth years passed). Luthor somehow knows from all this what kind of crystal to look up in his library, too. "Deductive reasoning, that's the name of the game," he says.
 * He gets one pass in the director's cut, however. He tried EVERYTHING ELSE first, with fire, ice, lightning, etc.
 * Black Dynamite brilliantly parodies the entire concept here.
 * Subverted in The Princess Bride: Vezzini uses this to "deduce" which glass contains poison ("Iocane comes from Australia, as everyone knows, and Australia is entirely peopled with criminals, and criminals are used to having people not trust them...") Arguably, he isn't actually trying to Bat-Deduce the location of the poison—he's just trying to get a revealing reaction out of the man in black. (Either that or he's just too caught up in his own cleverness to realize that he's thinking in circles.) The real irony is that all of his Bat Deductions lead to the right answer: He successfully proves that he can't drink from either glass.
 * Subverted with Jason in Mystery Team, who sometimes makes assumptions based on the smallest pieces of evidence. Played straight later with Jason connecting the murders to when he tells him to "Take a chill pill."
 * In Without a Clue, lampshaded. A mysterious number is given, and Sherlock Holmes uses a few long and complicated leaps of logic to deduce that it means a specific warehouse.

Literature
""4 symbolizes death, so 4-5 obviously means 'death finds you'[...]""
 * Deconstructed in a scene in Paul Auster's City of Glass, where it is used to show that the character doing it completely insane.
 * Joyfully inverted in Sherlock Holmes' The Adventure of the Yellow-Face. The title detective extrapolates a complex theory involving murder and foul-play to explain the case without having so much as set foot in Norbury to Watson. And then, rather than every leap of logic/intuition being correct—he turns out to be ENTIRELY wrong in all his deductions.
 * Holmes himself was invented, in part, because Arthur Conan Doyle was sick and tired of seeing detectives in fiction who always solved the case via this trope.
 * Harry's deductions about the Deathly Hallows in Harry Potter. Lampshaded by Hermione, who looks at him as if he's lost his mind when he comes up with it. Nevertheless, he turns out to be right.
 * Sir Nathaniel in Bram Stoker's Lair of the White Worm is an expert in this. When invited to tea in a villain's lair: "It is an old trick that we learn early in diplomacy, Adam -- to fight on ground of your own choice. It is true that she suggested the place on this occasion; but by accepting it we make it ours." He also deduces that despite being an antediluvian shape-shifting dragon-worm creature, she can still be relied on to fit their standard female stereotypes.
 * In Book Girl and the Famished Spirit, the Literature Club receives a mysterious letter written in a number code; Tohko immediately deduces the meaning based on what seems to be free-association.


 * Early in Journey to the West, Sun Wukong's teacher decides to tell Sun Wukong to meet him at the third watch through the back door to his chambers in order to learn the secret to immortality and Kung Fu superpowers. He communicates this by smacking him three times and then leaving the room through the main door with his hands clasped behind his back. Sun Wukong figures it out, naturally.
 * In The Lost Fleet captain Geary reasons why Syndics would delete software from evacuated base is the
 * The Department of Dead Ends in the work of Roy Vickers was described in its first appearance as an attempt to weaponise this trope. On one occasion, they caught a murderer by punning on his name.
 * Dirk Gently. He once came to the correct conclusion as a result of the insurance people describing an explosion as an "act of God".

Live-Action TV
"Robin: If you take the first three letters of those elements, it spells N-U-S ... but that doesn't mean anything. Batman: Reverse the order, and what do you have? Robin: S-U-N. Batman: Of course, that's got to be it! Robin: But what's it supposed to mean? Batman: Robin, I'm surprised at you. You're supposed to be studying French in school. What's the French word for sun? Robin: Soleil! Batman: Correct. The Riddler has left us a clear indication of where he intends to strike next. Back at Madame Soleil's wax museum!"
 * The 1966-68 Batman series made liberal use of this, as the various villains would usually leave clues for World's Greatest Detective, and the correct solution almost always required Bat Deductions. This turned pretty often with The Riddler.
 * Once, Batman solved one of the riddler's riddles that wasn't even spoken or written. Riddler used a wax-based solvent to dissolve a hole through the wall of a vault, and on doing a forensic investigation of the crime scene, Batman's chemical analysis revealed it to contain Nitrogen, Uranium, and Sodium:

"Kirk: Yangs? Yanks? Spock, Yankees! Spock: Kohms? Communists? The parallel is almost too close, Captain. It would mean they fought the war your Earth avoided, and in this case, the Asiatics won and took over this planet."
 * Also the IUPAC naming convention places Sodium's symbol as Na not S (which is Sulphur/Sulfur). So N, U, Na ...or Na-N-U: It's Mork!
 * The series was so aware that it was going to rely on this sort of thing that invoking the trope formed the backbone of the plot of the very third episode. The Penguin, being out of ideas for a heist, sends a random umbrella to Batman. His plan: Batman will analyze the "clue", use Bat Deduction to figure out what the Penguin is planning, and the Penguin will hear it through the radio transmitter hidden in the umbrella, and then go and commit that crime! A brilliant inversion, lampshading, and subversion all in one, though one wonders how the Penguin figured he would get away with a crime that Batman knew he would commit before he himself did...
 * The series actually got worse as time went by. Batgirl once deduced the plot of an entire episode based on the fact that her father was late getting home and that a new singer was in town.
 * In another episode, Riddler knockoff "The Puzzler" left a clue that "will make Batman and Robin really put on their thinking caps": a piece of paper with the single word "Puzzles". Cue extraordinarily Egregious use of this trope.
 * Mulder did this a lot in The X-Files.
 * This varied a lot on an episode-to-episode basis. One of the true non-paranormal detective episodes, "The Amazing Maleeni" about the magician who seems to decapitate himself for real during his act left all the clues in a breadcrumb trail and a sufficiently sharp viewer can deduce the conclusion and unravel the entire mystery just before Mulder gives the solution in the final reveal.
 * One of the main characters in The Others had his divination power work like this.
 * Used heavily in the early seasons of Star Trek: Voyager whenever an Anomaly of the Week needed to be explained.
 * Happened now and again in Star Trek: The Original Series. One example is this exchange from "The Omega Glory" about two warring factions, the Yangs and the Kohms:


 * An episode from the last season of Charmed opened with Billie deducting that, to search for her sister who was abducted by demons, she needed to find a powerful bloc that demons would work with. Simple - corporate America. And since she's read this story about a guy who was kidnapped as a child and now works with "corporate America," she's going to try a magic spell to see if he has anything to do with demons. And this works.
 * Stephen Colbert used this technique to twice pick the Oscar winners. He has a shockingly good success rate.
 * Considering how rare it is for an Oscar to be awarded purely on merit (among the rubrics used is whether or not an actor is "due", and no, I'm not kidding), maybe "shocking" is the wrong word.
 * Colbert parodied himself by using the technique to "pick" the winner of the 2008 Presidential Elections. He kept using starting points clearly designed to point to John McCain, but wound up picking Barack Obama every time. Even when he started on... John McCain.
 * Colbert and others generally use this kind of reasoning in parodies of Glenn Beck's chalkboard illustrations.
 * In one episode of Criminal Minds Reid correctly figures out who the murderer is by hypothesizing the murderer had multiple personality disorder, based on a single anomaly in a polygraph test, because the suspect got a control question wrong. Instead of concluding the subject failed math he went through the conclusion that on that one question a second personality took over (a phenomenon they had no evidence for) knew the answer to the question, lied about it (even though it had no incentive to do so on the first question), and that lying on the test meant that the suspect was indeed the murderer.
 * To be fair, Reid had already clued in that something was wrong: his first hint was the uncharacteristic behavior the suspect had after the test.
 * All That featured Detective Dan, who relied upon a combination of this and Insane Troll Logic.

Tabletop Games

 * The Mutants and Masterminds expansion book "Mecha and Manga" introduced the Conspiracy Theorist feat which lets players make Knowledge rolls on completely unrelated (and untrained) knowledge skills after rolling a 20 (or less with further ranks) on their previous skill roll. A series of successive high rolls quickly produces Bat Deductions as your character moves from Knowledge (Technology) to Knowledge (Civics) to Knowledge (Natural Sciences) to note that not only are devices in question mind control devices, but that the particular composition of police officers means the president must be on a secret visit, and that the peculiar white coarse hair caught on the boxes means that there's a diabolical plan by Dr. Silverhair, the transfigured ape turned Nazi, to kidnap the president.

Video Games
"Max: We're detectives, Sam, not mind-readers! Maybe we should ask Hugh Bliss. Sam: Mind readers! That's it!... No, that's not it. Max By the way, have you seen my copy of "Emetics" the handbook for multi-coloured happiness by Hugh Bliss? Sam: Colours!... No. Think, Max, think! Max: I know I had it this morning. Sam: That's it! "Morning"! In the ancient tongue of the mud-worshipping Kappalahotek tribe of the Serengeti, our word "morning" means "he who destroys the hypnotic rainbow man"! That's the word he fears the most! So this Roy G. Biv is the one person we've met who's never said the word "morning"! That means it's-- (phone rings, Sam answers) Sam: It's the Commissioner! Max: The Commissioner? I never did trust him! Sam: No, chucklehead, it's Hugh Bliss! Max: Never!"
 * While a very good game, Heavy Rain uses this
 * Even worse in L.A.Noire where in one case Cole deduces that Wait what? Even your Partner lampshades this.
 * A good portion of the Ace Attorney series is based on this. The player often figures things out before the lawyer, and vice versa. The hilarious bit is that it's acknowledged, multiple times, that Phoenix Wright is basically BSing furiously.
 * Umineko no Naku Koro ni: This is how Battler . One of the clues that Battler used was Knox's 6th: It is forbidden for the case to be resolved using accident or intuition, so Bat Deduction should easily be averted by the readers.
 * In Sam And Max Save The World: "Bright Side of the Moon", Sam figures out Roy G. Biv's identity through a long chain of reasoning that has nothing to do with the actual clue in his name (a mnemonic for the colours of the rainbow).
 * In Sam And Max Save The World: "Bright Side of the Moon", Sam figures out Roy G. Biv's identity through a long chain of reasoning that has nothing to do with the actual clue in his name (a mnemonic for the colours of the rainbow).


 * This is lampooned in Space Quest V. When Beatrice is infected by The Virus, Roger and his crew have no idea at first how to cure her, and can only use a cryogenic chamber to slow the infection. Later, however, Spike - a Face Hugger Roger befriended earlier - starts hopping on the chamber, and then the transporter; Roger somehow surmises from this that Spike is telling them to "initiate a manual control bypass to reverse the phase polarity of the interface grid and then use the transporter to reintegrate Beatrice's molecules." Cliffy seems to think that's Crazy Enough to Work and it does.

Web Animation

 * In the first season finale of Rooster Teeth short films, Matt leads Joel through a massive Bat Deduction that ties together all of the previous episodes with rather tenuous connections. One example is that the truck that hit him in "Catch" was made in Detroit, which has a high rat population, which is controlled through rat poison, which was put in their coffee in another episode... the end of this train of thought is the box/time machine from the first episode.
 * And in their series Red vs. Blue: Revelation, Sarge uses this to figure out that . The sequence starts out as Sarge being surprisingly clever with genuine deductive reasoning, but quickly devolves into this trope, as Grif looks on bemusedly.

Web Comics
"Sam: Helix, why is it every time you think, it's my head that hurts?"
 * Spoofed in this Irregular Webcomic strip, were the heroes totally get it wrong.
 * Happens in Freefall, when Helix uses this to find Sam.


 * Deconstructed humorously in this episode of The Non-Adventures of Wonderella, in which we see what happens when you overestimate your opponent's deductive skills.
 * Chainsawsuit has a character guessing what another wants—not that hard, because it's obviously the best idea ever.
 * Shortpacked shows a possible exploit.

Web Original
"Riley: Today's Friday, Coroner puts TOD about 12 hours ago, that makes it Thursday, or Thor's Day, Thor being the Norse god of Thunder. Thunder and lightning are formed when two weather systems of opposing charges come together. Charge begins with C, Weather Systems with a W. C and W, the intials of Cyrus Walker, local playboy and socialite who runs a thriving pork futures firm and was recently indicted for corporate fraud. The journalist who broke the story was Janet Smith, local reporter and wife, I think you'll find, of your suspect, Ted Smith, 375 Carinhood Road. Rodriguez: That's pretty much about it, he turned himself in this morning. Riley: Outstanding."
 * In the Loading Ready Run Rapidfire Comedy Sketches, they intermittently show a police detective following this sort of train of thought, eventually proven right by way of a much simpler solution.

"Hilo: Here's the battle map! Ackro: All I see, are, grease smudges! Hilo: The one close to me looks like an alien spaceship! Because the Martians have agreed with us that the ghost town's gotta go!... And the mushroom cloud-like [grease smudge] next to you... is the end of Muhammy al-Dracula! Ackro: And where are we gonna get plutonium to nuke Mecca from, a DeLorean??? Hilo: Snagnabbit, that's it! If we can't find plutonium for the bomb, we'll never convince the werewolves to come out during a crescent moon! Because they'll be showing Yogi Bear reruns if that happens!!! This completely ruins the whole plan!"
 * Morgan Freeman uses this in Bric-A-Brac Burning Man to determine who killed Dennis Hopper and how.
 * When Bikes Argue 2 has the following exchange:


 * Hence, Hilo realizes that Ackro is right in saying that it's preposterous for bicycles in a pole barn to nuke Mecca. But his reasoning doubles as both Right for the Wrong Reasons and Bat Deduction!

"For example, people like you can see an oven and grunt out loud, "oven is hot. Hot things hurt. Hurt is bad. It is bad to touch oven." The Super Friends see an oven and shout, "oven... heat... lava... Great Gotham! The Legion of Doom's headquarters is in the heart of a volcano! Let's roll!" But the most insane part is that they're usually right."
 * This Overheard bit of navigational wisdom.
 * Seanbaby, on Batman and the Riddler (in the animated Superfriends cartoon):

"Tom Hanks: Let's see here... we're in a tomb. Tomb... like Tombstone pizza, which is circular. Circular is the opposite of square... of course! To Saint Peter's Square!"
 * "The Editing Room" did a parody screenplay of Angels & Demons, in which Robert Langdon (referred to in the script as Tom Hanks) does this really often.


 * Ranger in Comic Fury Werewolf has an unusual brand of "logic". His deductions rely on a series of jumps in logic which qualify as this more often than they don't.
 * Facebook answers the Question in this way.

Western Animation
"Jeff: Wait a minute: butt sex! Chef: Butt sex?! Jeff: Butt sex requires a lot of lubrication, right? Lubrication. Lubruh... Chupuh... Chupacabra's the, the goat killer of Mexican folklore. Folklore is stories from the past that are often fictionalized. Fictionalized to heighten drama. Drama students! Students at colleges usually have bicycles! Bi, bian, binary. It's binary code! Chef: ... Who's having butt sex? Jeff: There's a huge ship of some kind in Earth's orbit! But why? Wait a minute: chaos theory! Chaos theory, it was first thought of in The Sixties. Sixty. That's the number of episodes they made of Punky Brewster before it was cancelled. Cancelled... Don't you see? The show is over! The aliens are cancelling Earth! Jeff: Whoever they are, if they're receiving messages, they might be sending them, too. Wait a minute: candy bars. They usually come in a wrapper. Just like you... wrap a Christmas present. Christmas happens when it's cold. Cold, as in Alaska - that's... with polar bears. Polar bears... pola... polarity! I can switch the polarity to see what transmissions are coming from the location this one is being sent to! Chef: THAT MAKES ABSOLUTELY NO FUCKING SENSE!!"
 * Batman, in the 1970s Superfriends cartoons, would routinely come up with some extremely convoluted link between the clues and the crime. It became especially pronounced if the Riddler was involved.
 * This is one of Darkwing Duck's signature detective skills: for instance, finding the location of the Fearsome Five's hideout from a breadcrumb—as opposed to, you know, looking for the giant flag indicating their hideout. Lampshaded by Nega Duck, who knew he would never see the giant flag and so planted the bread crumb.
 * In the Justice League episode "Legends", the Justice Guild of America, a team of heroes from a Silver Age Retro Universe, gets notice that the bad guys are planning a crime spree themed for the four classical elements. The Guild members immediately figure out what these refer to, even if they are only tangentially related to the elements themselves: The fire crime is the theft of the famed fire ruby (a gem), the air crime is the theft of an "antique flyer", the water crime is the theft of a new fountain being dedicated by the city's mayor, and the earth crime (this one is a doozy, and the biggest Bat Deduction of all) is the theft of the trophy for the clay court tennis championships. The League is pretty confused by this development, to be fair,.
 * The earth crime being the trophy for the clay court tennis championship makes a bit more sense when you consider that the criminal who commits it is The Sportsman.
 * In the episode "Cancelled", South Park's parody of Independence Day, the scientist (Jeff, for Jeff Goldblum) would fixate on a random element and follow a completely nonsensical chain of reasoning to come up with the solution. For example:

"Professor Farnsworth: Animatronio mentioned a fountain. That's a statue of Neptune, god of water. The number of points on his trident is three, or "tre". The "u" in his name is written like "v". "Tre", "V". "Tre"... Trevi! It's the Trevi Fountain! There can be no question! Leela: But, Professor-- Professor Farnsworth: THERE CAN BE NO QUESTION! "
 * If it wasn't obviously intended otherwise, you might think he'd already subconsciously come up with the right answers in a more logical intuitive way and needed to babble randomly until he managed to get a hold of them consciously.
 * Played with in an episode of Teenage Mutant Ninja Turtles when Donatello finds the bad guys by doing a long, drawn-out series of calculations... then looks up and sees all the fireworks.
 * Johnny Bravo is prone to doing this; one episode even features Adam West, who exhibits this kind of logic by interpreting a fortune cookie that said "Your heart's afire" to mean the Johnny's Momma was being held hostage at a golf course.
 * And then he interprets the flag sticking out of the holes as signs of a race of mole men who are plotting to create mole-human hybrids so they can Take Over the World.
 * Professor Farnsworth of Futurama uses this a lot in "The Duh-Vinci Code":

"Batman: Penny... Penny... Cent... Red cent... Copper! It's made of copper! Alfred: And "copper" is another word for "policeman"! Batman: And no tails means heads. Police... Head... Quarters! [...] Batman: Four quarters and one penny equal 101 cents, so... Police headquarters, room 101!"
 * Even better is the fact that he ignores the more obvious deduction, the Fountain of Neptune, also in Rome.
 * Naturally, episodes of Batman: The Animated Series involving the Riddler had this sometimes.
 * This exchange between Batman and Alfred in the Batmobile, where Batman has a handful of coins and the clue "Ask me no questions and I'll tell you no tales. It all makes sense when you add it up."


 * The silliest thing about this? Batman was going to go back there eventually anyway.


 * Same episode, leads into the above one. Three computers crash around Gotham, displaying only a riddle on screen: "Where does a 500-pound gorilla sleep?" "What's worse than a millipede with flat feet?" "How do you fit 5 elephants into a compact car?" Train of logic: the Riddler doesn't usually use such commonly known riddles meaning the answers to the riddles are a red herring. The riddles themselves all contain numbers: 500, 1000, 5. Convert to roman numerals and get D,M,V... the Department of Motor Vehicles!!!
 * Underdog. Apparently, "A rhyme/In time/Saves nine" means "Underdog should come to the town's diamond store to stop a heist." Ah, yes. "Nine... That's a baseball team, they play on a diamond, and time... like Big Ben... Ben's Jewelry Store!"

Real Life

 * ARGs often work like a combination of this and Trial and Error Gameplay. Each clue can be extrapolated from in order to lead to the next, usually in some completely random way. For example, a set of numbers could symbolize any number of different things. Often the only way to figure out where the trail leads is to try every possibility until you find something that looks like another clue.