Taking the Third Option is one of the central, if not even the single most important principle of Buddhism. Born as a prince and having lived all his life in a palace, Siddhartha Gautama lost all joy in the riches and pleasures of his life when he realized that all people will eventually become old, sick, and die. So he became a wandering ascetic, hoping to find spiritual happiness by ignoring everything material and only meditating all the time. But even though he tried harder than anyone else, it only made him starve and become sick, so he gave it up as well and started to eat again and take care of his health. Only when he tried to find a balance between comfort and living a simple life did he gain enightenment and became the Buddha. Teaching this Middle Way to the other ascetics that he was living with is regardid as the birth of the Buddhist community.
When Kuchisake-onna asks you if you think she's pretty, especially after she reveals her Glasgow Grin, honesty is just plain suicidal. Telling her she DOES look pretty isn't a good idea either (as "kirei", the word she uses for "pretty", also means "to cut with a knife"). However, you can tell she looks so-so, or give her candy, or throw candy in another direction, or ask her if she thinks you're pretty. Most of these will just confuse her. Also she LOVES candy. Due to Japanese politeness, you can also tell her you're busy or need to get to an appointment, and she will apologise for her rudeness and leave.
There's an old story about a princess that was forced by an evil witch to marry one of her ugly sons, so they will become king. The princess must make a statement, and if that statement is true, she will marry son A. If it's false, she'll marry son B. After some deliberation, the princess says "I will marry son B". The evil witch is unable to come up with a solution, and lets the princess go free.
There's a fairy tale in which a farmer brags about his clever daughter, and the king agrees to marry her if she can solve a riddle; else the farmer has to pay for his bragging. The riddle is that she must come to his palace to meet him neither during the day nor night, neither naked nor clothed, neither hungry nor fed, neither on foot or with a ride, and neither on the road nor off it. The farmer's daughter arrives at dawn/dusk depending on the story, with a fishnet wrapped around her, having drunk her fill of water, being dragged by a horse on the edge of the road. The king marries her.
There's a similar story where, instead of arriving like that, the daughter simply didn't show.
The way I heard it the requirements were neither nude nor clothed, neither riding nor walking, neither day nor night, and she must bring a "gift that is not a gift". She comes at dusk/dawn with a blanket covering her so she was neither clothed nor nude, with one leg over a goat so she was not quite riding yet not quite walking, and in a small cage she had a bird that as she gave it to him she let it go free. On their wedding day the king made her promise not to interfere with his kingly duties, one day she does and her punishment is to be sent back to her father, but as the king still loves her, he allows her to take with her one gift. She chooses to take him. The king decides not to make her leave.
Another solution I've heard is to come during a solar eclipse, with a blanked wrapped on, having drunk milk, and arriving either by horse-drawn sleigh astride the road edge, or arriving by a boat. The king marries her.
In the story, The King's Equal, a dying king tells his son that he can't take the throne until he marries a woman who he admits is as beautiful, intelligent, and rich as he is. Eventually, a gorgeous young peasant girl shows up, and the prince says that she's "the most beautiful creature [he's] ever seen." She doesn't want anything because she has her friends, while he wants the crown. And she knows something he doesn't -he's very lonely. The prince admits that she's his equal... and the woman announces that, in fact, he has just admitted that she's better than him in every way, and sends him off to care for her goats for a year while she gets the kingdom back in order. He comes back a better person and they get married.
A 14-year-old Lebanese girl named Rafqa Pietra Choboq Ar Rayès was stuck between two possible Arranged Marriages. Her stepmother said she should marry her brother (aka the kid's uncle); her maternal aunt, however, said the girl should marry her son. After witnessing the two women fight it out, Rafqa locked herself in her room to pray and think about what she should do... and took the third option she had left: running off to a nearby Christian convent and becoming a nun, not just to escape the marriages but because she already wanted to do so. She became the first Lebanese female Catholic saint.
Some time ago, a prince offered those who had committed a crime a chance to either die by being hanged or being decapitated with a sword (which was considered honorable), which consisted in saying something true, non-related to the prince. Most people failed due to the prince, who just declined everything said and condemned them to die by the mob. One day, an old man was being judged, after being asked the question, he said "I'll be hanged". If he got hanged, then what he said would be a truth, so he should be decapitated. But then if he was decapitated, he would have been saying a lie. The prince was impressed by such a demonstration of wit, and let the old man live.
The Pharisees tried several times to try and turn Jesus' popularity against him. In one example, they asked whether the Jews should pay the oppressive taxes imposed on them by their Roman overlords. Answering yes would anger the Jews; answering no would bring down the wrath of the Romans. Jesus pointed to Caesar's face on a coin and advised the listeners to "Give Caesar what is Caesar's and God what is God's." Since both sides at least claimed not to be interested in what was the other's, everyone was happ... No one found anything to complain about.
There is a Russian folk story of an old man sentenced to death by Czar. The Czar grants him one wish. The man says: "Give me five years and if I manage to teach a horse to speak, let me free". Some of his friends protest and say he should have gone to death proudly while some say he should have pleaded mercy from Czar. The man replies: "See, I am an old man, and within five years a lot of things may happen. I may die, the horse may die or the Czar may die. And there is always the chance that the horse will learn to speak."
In The Bible Two young women who lived in the same house and who both had an infant son came to Solomon for a judgement. One of the women said that the other, after accidentally smothering her own son while sleeping, had exchanged the two children to make it appear that the living child was hers. The other woman denied this and so both women claimed to be the mother of the living son and said that the dead boy belonged to the other. After some thought, King Solomon called for a sword to be given to him. He declared that there is only one fair solution: the live son must be split in two, each woman receiving half of the child... Upon hearing this terrible verdict, the boy's true mother cried out, "Please, My Lord, give her the live child—do not kill him!" However, the liar, in her bitter jealousy, exclaimed, "It shall be neither mine nor yours—divide it!" Solomon instantly gave the live baby to the first woman, realizing that a true mother's instincts were to protect her child, while the liar revealed that she did not truly love the child; not knowing which one was which at first, he simply decided to pretend to take this violent third option and flush the real mother out with it.
