Impossible Task

"Ask him to find me an acre of land Between the salt water and the sea-strand, Plough it with a lamb's horn, Sow it all over with one peppercorn, Reap it with a sickle of leather, And gather it up with a rope made of heather, Then he'll be the true love of mine."

- Scarborough Fair, Child # 2

The Impossible Task is a favorite theme in myths and legends, folklore and Fairy Tales the world over, and is Older Than Feudalism. The task might be undertaken to win a boon, or a bride, to gain land, to break a Curse, because everyone will know about it if you do it, to prove your worth to Baba Yaga (who may agree to be your mentor if you succeed), or because your Evil Uncle wants you—the rightful heir—out of the way. Some creators try to set up one as the Fantastic Fragility flaw.

In general, the person who assigns the task does not expect the hero to succeed and is just trying to get rid of them or to make an excuse to not keep their end of a deal. Sometimes the Impossible Task is a quest, often involving killing an unkillable beast, but in other cases the task is a simple paradox or riddle.

Sometimes, the one making the task will be bound by their Promise should the hero succeed, or face dire consequences if they refuse. On the other hand, it may be a form of Dude, Where's My Respect? when the king really doesn't want to hand out the Standard Hero Reward, and the king may go on, and on, with the Impossible Tasks until finally one blows up in his face, or he decides You Can't Fight Fate.

On the other hand, sometimes the task-giver is really quite pleased at the hero's success -- they can now be sent out again! And again. And again.

Classic examples:
 * Carrying water in a sieve (stop the holes with mud or moss, carry something able to hold water in the sieve)
 * Sorting a huge pile of grains and lentils in a single night (if you helped a wounded bird earlier, it will call its friends to help you)
 * Making a rope of ashes (make a rope out of straw, then burn it)
 * Appearing before the challenger neither naked nor clothed, neither riding nor walking, neither in night nor day... etc. (come wrapped in a fishing net, with one foot on a goat, at twilight)

Sometimes the challenge is answered like a riddle (e.g. when told to "Bring fire wrapped in paper," the hero returns with a paper lantern), sometimes by finding a witty way to demonstrate its impossibility (e.g. the king tells the peasant to bring him "yogurt made with bull's milk;" the peasant's daughter arrives the next day saying, "My father can't bring you that yogurt you asked for because he's giving birth to a baby.")

These fall into in three categories.
 * 1) Feats that should be too hard, but the hero is just that Badass (like killing one hundred Philistines).
 * 2) Feats that sound like they break the laws of physics, but the hero treats it as a riddle, exploits a loophole in the requests (like carrying water in a sieve) or succeeds purely because he didn't know it was supposed to be impossible.
 * 3) A Chekhov's Gun magic spell solves the problem (like in the Grimm's fairy tale of the seven servants, or Aladdin). The Mad Scientist's Beautiful Daughter is useful for that.

In The Kalevala example, the magic is used to parody the whole thing.

Sometimes, the hero doesn't solve the task at all, but rather by being kind to others before the task is given. Be it befriending Androcles' Lion, freeing a Benevolent Genie, or otherwise gaining the Disproportionate Reward of a Sidekick Ex Machina.

Another recent variant, if the Curse lasts long enough, is to wait until modern or future technology makes the impossible possible. Almost always something the witches and warlocks didn't count on. See Post-Modern Magik.

Related to No Man of Woman Born, We Do the Impossible and Cutting the Knot. The Engagement Challenge is often an Impossible Task. The Snipe Hunt can be a comic form of it.

Not to be confused with the Impossible Mission, which is an entire plot with its own set of tropes.

Anime and Manga

 * Kenichi: The Mightiest Disciple has Takeda tried to convince James Shiba to train him. James promptly gives him several impossible tasks to get rid of him. Takeda completes the tasks anyway, and James takes it as a sign that fate must want him to train Takeda.
 * Since Mikado of Hayate the Combat Butler wants others to think that there's a possibility of gaining his inheritance from the rightful inheritor, he's set up several 'Impossible Tasks' for them.
 * The first, make Nagi cry and apologize,.
 * After that, it was to steal a Mineral MacGuffin her Battle Butler carried. . Now she's having to learn to live without the backing of the inheritance.
 * In AKB49: Ren'ai Kinshi Jourei, producer Akimoto of the idol group AKB48 likes to give tasks which are effectively impossible to the trainee members to force them to improve themselves, such as requesting them to attract a full house performance within 2 months at the price of 10000 yen per ticket (performances by regular members only cost 3000 yen per ticket) or face disbandment.

Comics
"King: Come to me, not dressed, not naked, not on a horse, not by carriage, not on the road, not off the road, and if you do, I'll marry you."
 * In Preacher (Comic Book), Jesse Custer punishes one of the Big Bad's flunkies by compelling him to go sit on a beach and count three million grains of sand.  As far as Custer's punishments go, this is getting off lightly.
 * Erstwhile has this in paradox form, while telling "The Farmer's Clever Daughter".

"Papa Smurf: Firstly, each morning, drink a pint of dew collected from a web woven by a male tarantula. Secondly, find a moonstone at the precise moment the sun is in eclipse. Thirdly, crush the moonstone delicately with your little finger while uttering cries of joy. Fourthly, wait for the powdered moonstone to turn to salt (this may take a hundred years). Fifthly, drop a pinch of this salt on a comet's tail. Sixthly, at the same time, get a tomcat to holler three times, 'SECAKEJUKEUACEHEPAOZREUPAUR". Seventhly, do not be discouraged, Eightly..." (There's more to it, but the protagonist leaves before he can finish.)
 * Answer: show up stripped to the waist, on a mule, that's halfway off the shoulder of the road.
 * In The Smurfs story "The Astrosmurf", the title character's first attempt at finding a way to travel to the stars is to ask Papa Smurf for advice. Papa Smurf has something in his spellbook called, "How to Travel Through the Macrocosm", a multi-part, complicated (to say the least) ritual:

Fairy Tales
""I have emptied a dish of lentils into the ashes for thee, if thou hast picked them out again in two hours, thou shalt go with us.""
 * "Rumplestiltskin", where the (eventual) princess is forced to spin straw into gold. Also when the eponymous character asks her to guess his name.
 * Child Ballad #2 ("The Elfin Knight"), and its folk-processed descendant "Scarborough Fair." See page quote.
 * The horde of chores heaped upon Cinderella by her Wicked Stepmother were of this nature. Not impossible in and of themselves, but all heaped together they make an insurmountable task.
 * In Aschenputtel (the German version of Cinderella), the Wicked Stepmother set such a task to let her go to the ball:


 * The Russian fairy tale of Vasilisa The Beautiful involves many of these. Vasilisa's Wicked Stepmother sends her to fetch fire from Baba Yaga, expecting the girl to be eaten alive. Baba Yaga instead sets her to work on tasks that include threshing a roomful of wheat, stripping 10,000 ears of corn, and picking out a wagonload of poppy seeds from black flour dust, each in a single night. With the help of her magic doll she completes all the tasks and retrieves the magic fire, and when she brings it home, its light burns her wicked stepmother and stepsisters to ashes.
 * A Jewish Fairy Tale: the king told some guy to tell him the number of hairs on his head, the number of stars in the sky, and the center of the earth. The guy plucks a hair from the king's head and says "one fewer than there were before", the number of stars in the sky is equal to the number of hairs in his donkey's tail, and the center of the earth is where his donkey stamps its foot. When the king gets upset with those answers, the guy basically says "if you're so smart, then you tell me." He gets to go free.
 * The stepmother in The Well At the World's End sends her stepdaughter to the title well with a sieve.
 * The stepmother sends her stepdaughter into the winter woods to get strawberries in The Three Little Men In the Wood.
 * One story of the peasant's clever daughter is Grimms' The Peasant's Clever Daughter
 * In The Black Thief and the Knight of the Glen the stepmother plays a game of cards with her stepsons so she can force them on an impossible quest.
 * In the Russian Fairy Tale Go To I Know Not Where, Bring Back I Know Not What, the command in the title was used to get rid of a husband. (Fortunately, his wife could turn into a bird and fly off.)
 * In another version she had her house turned into a hill and herself into a rock instead, unsealed only when her husband came back.
 * From the Arabian Nights: Aladdin gives the sultan a bunch of large jewels in exchange for the sultan's daughter's hand in marriage. The sultan tells Aladdin to bring 40 slaves carrying 40 trays all filled with those kinds of jewels and then he will consider. The sultan considers this impossible. Aladdin of course has a genie, so problem solved.
 * Princess Kaguya's impossible tasks
 * In The Wonderful Birch, the Wicked Witch takes her daughter to the feast, and orders her stepdaughter to pick barleycorns from the cinders while she's gone.
 * In The Fish and the Ring, Vasilii the Unlucky, The Devil With the Three Golden Hairs, The King Who Would Be Stronger Than Fate, and many other fairy tales, a man who discovers finds his child doomed to marry a poor child tries to kill them with many tasks, before and after the wedding; in the end, he fails.
 * In The Grateful Beasts, Ferko is cut all the corn in a single night, gather it all into barns the next night, and summon all the wolves in the land. It stops with the wolves because, well, they're wolves.
 * The fairy tale type Kind and Unkind Girls often features this.
 * In The Three Little Men in the Wood, the stepdaughter is sent out to gather strawberries in the snow. She meets and is polite to the title men, and they send her to a place with strawberries and give her more blessings. So the Wicked Stepmother sends her own daughter, who is rude and so finds nothing
 * In Frau Holle, when the girl drops her shuttle in the well, her Wicked Stepmother orders her to fetch it out again.
 * In The Two Caskets, the Wicked Stepmother sets a spinning competition between her daughter and her stepdaughter, with the first getting good flax and the second coarse stuff that no one would spin.
 * Many, many folktales of both European and Chinese origin feature a number of brothers with improbable talents given impossible tasks for fame, fortune, the Emperor's service or the hand of a princess. Sometimes they resemble each other closely enough to pass for the same person capable of a wide range of miracles.
 * The third classic example is from a Swedish saga, in which the full list of conditions is that the heroine cannot visit the king by foot, by horse, in a wagon, nor in a boat. She could not visit him either dressed or undressed. It could not be day or night, a month or a year, and the moon couldn't be waxing or waning. As described above, she wore a fishing-net, balanced one foot on a sledge and the other on a goat, and went at dusk. She also went on the third day of Yule, which was considered to lie outside the normal count of the year.
 * Prince Conn-Eda loses a chess game with his evil stepmother, and her geas (her binding condition on Conn-Eda that is her right after she's won) is that he go to the land of the fairies and take the black steed and supernatural dog of the king of the fairies, and return to her with them within a year and a day.

Film

 * From Monty Python and the Holy Grail: "Then, when you have found the shrubbery, you must cut down the mightiest tree in the forest... with... a herring!" *Scare Chord*
 * Also used in the "Happy Valley" sketch on Monty Python's Previous Record. To quickly get rid of any suitors who go after his daughter, King Otto sets them the task, "Tomorrow at dawn, armed only with your sword, you must climb to the highest tower in the castle, and jump out of the window." When the queen gets sick of this, he is forced to change the task to something a bit easier - going into town and buying some tobacco.
 * For a modern film version, Chandler Jarrell (Eddie Murphy) in The Golden Child is given a glass of water. He is told he must retrieve an item from across a cavern without spilling one drop of the water in the glass. He somehow manages to keep the glass of water after passing through all of the obstacles until he's standing in front of the hollow holding the Ajanti Dagger. When he reaches for the dagger the fire flares up, foiling him. He drinks the water and the flames die down, allowing him to grab the dagger.
 * A visual version of this trope is the third challenge from Indiana Jones and the Last Crusade—the bridge across the ravine doesn't seem to be there at all until you do what you think is impossible and have enough faith to step off the ravine. It's then that you discover the bridge was there all along, just painted so subtly you couldn't tell it from the far ravine wall. There's also a very powerful metaphor for faith in that visual riddle: faith is sometimes described as jumping off a cliff and landing safely in midair.
 * Since there is no notability, I'll mention a Turkish movie that had a very strange subversion to it. Set (and made) in 1991, one of the side-plots of the film involved the lover of the protagonist's daughter trying to convince the protagonist to let him marry her. The protagonist dismissively tells him to bring the feather of a phoenix. The lover, despite fully aware of the impossibility, doesn't argue against because he doesn't want to appear as a naysayer. He eventually returns (with a feather that obviously came from a chicken), and although the protagonist is not fooled, he still judges the lover to be one of the few people around him who's not after his money (the main plot). In the end, however, the whole thing turns out to be a Shaggy Dog Story because the daughter moved on to a rich socialite.

Literature
"Illyan: Do you know all those old folk tales where the Count tries to get rid of his only daughter's unsuitable suitor by giving him three impossible tasks? Ekaterin: Yes... Illyan: Don't ever try that with Miles. Just...don't."
 * In the book "Ironside" by Holly Black the pixie Kaye is forbidden from seeing the one she loves until she can find a faerie that can tell a lie, but promised his hand if she can. She solves this by.
 * The book Impossible by Nancy Werlin is based off of the Scarborough Fair song, explains how it came about, and the entire plot is this trope.
 * Discussed in A Civil Campaign by Lois McMaster Bujold:

""If you can slay the thorny Boar of Borythorn, she is yours," grinned a traveler. "But there is no thorny Boar of Borythorn, which makes it hard.""
 * In The Phantom Tollbooth, shortly after arriving in the Mountains of Ignorance, the protagonists meet a gentleman with no face who asks them to complete some impossible tasks: one of them is to carve a hole through a rock with a needle, one is to move a pile of sand with a pair of tweezers, and one is to empty one well into another with a dropper. After Milo uses a magic math-solving pencil he received from the Mathemagician to realize it would take thousands of years to finish the tasks, the man reveals himself to be the Terrible Trivium, one of the Demons of Ignorance and the anthropomorphic personification of wasting time.
 * In Stardust by Neil Gaiman the protagonist is challenged by a crush to bring back a fallen star from the magical land outside their town in exchange for her hand. Subverted in that she didn't actually expect him to try, much less succeed, and they didn't get married when he did.
 * In The Silmarillion, Beren is told to return to Doriath with a Silmaril in his hand if he's to be allowed to marry Luthien. Part just-that-Badass, part Exact Words; with Luthien's help (and by "help" we mean she did most of it) he gets further than he could possibly have been expected to get, but he is called "Beren One-Hand" for a reason...
 * In The Brothers' War, the King of Argive decrees that any suitor for his daughter must move a huge boulder across the town square. Urza builds a machine to lift and transport the stone, declaring that he had moved it with his mind.
 * The title story from The Practical Princess (and other liberated fairytales) features the titular princess trying to get rid of her unwanted suitor by sending him on these. (The two tasks, a fire-proof cloak and a jeweled branch, are reminiscent of those used by Kaguya-hime in the Japanese legend, and like Kaguya the princess sees through the fakes offered.)
 * In Inheritance Cycle, dragon riders were given impossible tasks to get them really frustrated so they'd learn to use magic. It never mentioned whether or not they actually solved the tasks.
 * In the Mr. Men books, doing this is Mr. Impossible's specialty. When asked if he can climb the largest tree in the forest without help, he walks up the tree. When asked if he can stand on one hand, he stands on no hands. (No feet either.) He solves a complex multi-part math problem at a schoolhouse in seconds (in his head), and reads a book to the class while holding it upside-down; in short, if told something is impossible, he can do it.
 * In Robert Silverberg's story "Double Dare", a team of Earth engineers and a team of alien engineers are engaged in a challenge where each is to duplicate some feat of the other's technology. Both sides cheat by presenting a rigged demo of a device they can't actually build. Both teams, not knowing that what they're trying to do is supposed to be impossible, succeed.
 * In the story "The King of Katoren", a young Stach is given seven tasks, each one imposibler than the last, to complete if he wants to become the titular King of Katoren. Those tasks are selected among the worst creatures, aberrations and illnesses that plague the people of the country. To make it impossible Up to Eleven, the last task is to sit on a monument cursed so that only can rest on it. Needless to say, all of them are solved.
 * In The Dragon Hoard one of the tasks is to empty an entire lake into a single jug.
 * Theoretically, the evil master in Krabat can be defeated easily - but he twists the words of the condition to his advantage. If a girl who loves one of the master's students asks on New Years' Eve to let him go, this would do the trick. However, she has to recognize her boy for this -
 * Gest is challenged to do this  in Power of Three by Diana Wynne Jones.
 * The Duke in The 13 Clocks sets impossible tasks to suitors who wish to marry his niece, the Princess Saralinda:


 * That one just begs for Loophole Abuse in the form of designating any random boar in Borythorn, the 'thorny Boar', even if you have to pay several locals to publicly proclaim it as such, and then shooting it. After all, its incredibly easy to fill a vacant position.

Live Action TV
"Tony: What is it with you people? What kind of twisted upbringing did you have? You know, why can't you just say, 'Oh, that'll be 100 gold coins'? Why does it always have to be, 'No! Not unless you lay a magic egg, or count the hairs on that giant's ass!'?"
 * From The Tenth Kingdom:

Mythology

 * The labors of Hercules are a classic example.
 * In Journey to the West, The Buddha asks Sun Wukong to jump out from his palm. It turns out to be impossible because The Buddha's palm engulfs the entire universe.
 * Psyche is given several of these tasks by a jealous Venus in the myth of Cupid and Psyche.
 * There's a certain African myth... a man gave his boys the task to see who would inherit his farm. He told each boy to go out and buy objects so that he could fill a room. The first two boys tried to do it with grain and feathers (if memory serves). They failed. The third son took out a candle and match, and filled the room with light.
 * The Norse gods needed to create a chain that could hold the Fenris Wolf. Thor's two attempts to forge such a chain failed, and the Wolf was becoming a major threat. They sent a message to the dwarves, who created an enchanted chain made out of the sound of a cat's footsteps, the roots of the mountains, the breath of a fish, and the sinews of a bear. It did the job.
 * In Norse legends, Aslaug is given an impossible set of conditions to arrive at the castle and meets them.
 * Another example of the Perseus story has King Polydectes sending Perseus to bring him the head of Medusa because Polydectes wanted Perseus's mother Danae, whom Perseus was very protective of, and wanted Perseus out of the way. When Perseus comes back with Medusa's head, he finds out that Polydectes had enslaved and abused Danae in his absence, and proceeds to turn Polydectes to stone with Medusa's head.
 * In the Mayan myth Popol Vuh, Hunahpu and Xbalanque are assigned several tasks of these during their descent to Xibalba (the Underworld). One of them was to keep a cigar lit a whole night without burning it out. They attached fireflies to the end of the cigar so they would appear lit.
 * An example that may be a parody: In the Finnish epic The Kalevala, Väinamöinen is a mighty sorcerer and bard who is utterly inept in love. One girl he flirts with tells him she will never marry him unless he cuts a swan in half with a knife without a point, and knots an egg with an invisible knot. (In other words, when hell freezes over.) Väinamöinen, being both clueless and a wizard, proceeds to complete both tasks with his magic. Then she says she won't marry him unless he pulls birchbark off a stone and breaks off poles from a piece of ice without a chip flying off. He uses magic to do both immediately. Then she says she can't marry him unless he builds a boat out of her distaff and gets the boat in the water without anyone touching it. He uses magic to do this easily as well...but an evil spirit causes him to accidentally cut himself with his axe, and he has to go on an adventure to heal his wound, by which time he has forgotten about her. (There are a lot of moments in The Kalevala that seem like parodies of myths.)
 * Louhi, the Mistress of Pohjola also gives type 1 impossible tasks to men who seek to marry her beautiful daughter. This too was related to Väinamöinen's adventures, but ultimately it was his blood-brother Ilmarinen who was Badass enough to fulfil every request and got the girl (until her wickedness got her eaten by bears, but that's another story).
 * Yet another example is not-yet-King David being told by King Saul that he can't marry Princess Michal unless he brings the foreskins of one hundred dead Philistines. David tops him by bringing two hundred.
 * A poem tells the story of the Abbot of Canterbury being summoned by the king for execution, for being able to keep a better household than the king does. The king is persuaded to give him his freedom if he can answer three impossible questions and to give him a year to seek the answers. Eventually the Abbot returns and answers all three: "How much am I worth (ie, how much money do I have)?" (Twenty-nine pieces of silver; even Jesus only sold for thirty.) "How quickly can I ride around the Earth?" (Keep pace with the sun, and you should make it in twenty-four hours.) "What am I thinking?" (You're thinking I'm the Abbot of Canterbury, when in fact I'm his clever servant. Please don't kill him.)
 * Subverted in the story of Naaman and Elisha. Naaman is a commander in the Assyrian army, but he suffers from leprosy. Having been told that Elisha can cure him, he goes out to the prophet to ask for assistance. Elisha shrugs and sends a messenger who says, "Go dip yourself in the Jordan River seven times"—a trivial task, except that its very triviality makes Naaman furious. He's about to refuse when his servant asks whether he wouldn't have attempted any difficult task required (in one literary version, "if he told you to go climb a mountain of glass"). Humbled, Naaman goes and gets his cure.
 * A Roman Vestal Virgin was accused of having had sex, a capital offense. To prove she was still a virgin, she offered to carry a sieve full of water from the Tiber to the Temple of Vesta "in proof of her perfect chastity". (Given that the accusation was political in nature, she may have had help to accomplish the task.)
 * In some Middle Eastern story, a King gave a challenge with a great prize if someone could get a valuable gem that's in the middle of a large carpet without tools or setting foot on the material. Many people try stretching as far as they could and failed, until one humble person realized that the challenge didn't prohibit touching the carpet with anything other than feet. So, he simply rolled up the carpet until he got halfway and simply picked up the gem.

Tabletop Games

 * In certain editions the Dungeon Master is expected to provide challenges like this should Dungeons & Dragons players want to create powerful permanent magical items. The win conditions are generally fairly lenient, though.
 * Paranoia missions tend to be this, especially after secret society goals and personal agendas are figured in. The game's stance varies from "literally impossible" to "we have no idea how to succeed, but acknowledge that sufficiently devious PCs will come up with something" to "the PCs could succeed by doing X and Y and Z, it's just ludicrously unlikely that they'll be lucky and virtuous enough to actually pull all that off".

Theater
"Cyrano: Come now, bethink you!. . .The fond hope to be Beloved, e'en by some poor graceless lady, Is, by this nose of mine for aye bereft me; —This lengthy nose which, go where'er I will, Pokes yet a quarter-mile ahead of me; But I may love — and who? 'Tis Fate's decree I love the fairest - how were't otherwise?"
 * Shylock's "pound of flesh nearest the heart" is related; in this case, it's the villain who is forced into either doing an impossible task, or giving up what is due him.
 * Skillfully subverted with Cyrano De Bergerac: In Act I Scene V, Cyrano claims that fate has decreed that he, being The Grotesque because of his large nose, must love the most beautiful woman there is, implying an Impossible Task. The truth is, given his Mommy Issues, Cyrano himself has chosen the most beautiful so he will fight knowing that he cannot win her love.

Video Games

 * Referenced in Odin Sphere, where Rebellious Princess Gwendolyn warns Cornelius that her father gives people tasks like these all the time.
 * The story for the 8th Touhou Project game, Imperishable Night, is heavily based on the legend of Princess Kaguya mentioned above. The final stage is even called "Five Impossible Requests", and Kaguya's spellcards are named after the five requests from the legend. The Bonus Boss of the game, Fujiwara no Mokou, is the daughter of one of the men who was given the impossible request.
 * In fact, her father was the only one to actually succeed in his task!
 * The manual of Microsoft Flight Simulator claimed it was impossible to fly under the Golden Gate bridge. It was possible.
 * In Etrian Odyssey III: The Drowned City, the ninja Kirikaze is sent to complete these so that her master might earn the right to marry Princess Kaguya.
 * In Turgor the player is given such tasks by Mantid and Warden.

Web Comics

 * Subverted and played straight here in The Curious Adventures of Aldus Maycombe - the faerie king is Genre Savvy, but it doesn't help him much.
 * Keith, from Twokinds is expected to bring the High Templar Trace Legacy back with him so that the conditions of his exile will be revoked, more or less "You can come home if you're bringing George Bush with you for dinner."

Web Original

 * The quest in Year Four of The Questport Chronicles: to rescue the Lost Lady from the netherworld, which requires help from vampires (thankfully, one of the heroes is a vampire) and voluntary Demonic Possession.

Western Animation

 * In Futurama, the Robot Devil challenges Leela in a violin contest, with her having to use a solid gold fiddle. Fry does point out that a solid gold fiddle "would weigh like a hundred pounds and sounds really cruddy." The Robot Devil admits to this, stated that it's "mostly for show". Leela does beat him though - over the head with the extremely heavy fiddle.
 * A modern parody may be the South Park episode "The Wacky Molestation Adventure." Kyle's mom tells him he can't go to a concert unless he cleans out the garage, shovels the snow out of the driveway, and brings democracy to Cuba. Of course he succeeds at all three.
 * He still doesn't get to go, being told specifically that they never expected him to be able to pull off that last one. Kyle decides this is unfair and applies some lateral thinking: calling child services and telling them his parents molested him so they'll get arrested and he therefore won't need their permission. It works.
 * Some of the Grimorum Arcanorum's spells in Gargoyles seemed to have this as spell conditions, until modern technology made the impossible possible, so to speak.
 * The most obvious is the one that woke up the sleeping gargoyles: the castle had to be lifted above the clouds. Xanatos literally does that, moving it brick by brick to the top of a tall building.
 * The terms of Zuko's banishment in Avatar: The Last Airbender. "Find a nigh-all powerful person, catch him, and bring him back, and then you can come home. Oh, and he's been missing for a hundred years."
 * In a US Acres segment of Garfield and Friends, Orson and Wade set up a restaurant that's guaranteed to serve any food you order - if they can't make it, you get free food for a month. Roy attempts to take advantage of this with several attempts at Impossible Orders... and then gets served exactly what he orders, to his own shock. He eventually wins with "an elephant foot sandwich with mustard". Even though Orson and Wade had found an elephant, it wasn't theirs to kill and put in a sandwich, so to screw with Roy, they just showed him the elephant and pretended that they were out of mustard.

Real Life

 * The University of Chicago Scavenger Hunt traditionally has an impossible task or two among the list of things to find, make, or do. One year it was "build a working nuclear reactor in a shed on the Quad", which, in best Impossible Task fashion, turned out to be not quite as impossible as the organizers had expected.