The Great Sultan of India has three sons: Hussein,the oldest; Ali, the middle; and Ahmed, the youngest. The Great Sultan also cares for his niece, the princess Nouronnihar, whose father had died.
The Great Sultan had planned to marry Nouronnihar to a foreign noble, but his sons all want to marry her. Knowing the youngest two would not cede her to Hussein simply because of his seniority, the ruler suggests she choose her own husband. They refuse to comply. Thus, the Great Sultan stages a competition: each prince will travel to a faraway land to collect the greatest rarity he can find. Whoever brings back the most valuable item will be granted the princess's hand. Eager, the princes set off immediately.
Prince Hussein travels to the kingdom of Bisnagar, where he finds a merchant selling a plain-looking carpet for a huge sum of money. He inquires after it, to learn that the carpet will transport its owner wherever he pleases. Though he knows this gift would likely win the contest, he is skeptical, so the carpet merchant promises to test it with him. Hussein agrees, and he and merchant sit on the carpet and are transported to Hussein's lodging in town. After buying the carpet, Hussein remains in the kingdom for a long time, knowing the carpet will transport him back home whenever he is ready.
Meanwhile, Prince Ali travels to the kingdom of Persia, where he finds a merchant selling a strange ivory tube for a huge sum. He inquires after it, to learn that one can see anything in the world by peering into the tube. To test it, Ali wishes to see his father and then Nouronnihar, and then looks into it. It works. He then buys the wonderful tube, and heads back home to meet his brothers.
Finally, Prince Ahmed travels far away to the kingdom of Samarcand, where he finds a merchant selling a small, unremarkable artificial apple. The merchant insists that the apple can cure absolutely any disease with one smell, and that it had saved practically everyone in the city at one time. When Ahmed asks for proof, many passersby attest to its power; however, Ahmed does not believe it until he sees the apple cure a sick wife with his own eyes. He then buys the rare apple and returns to meet his brothers, sure of his coming success.
When the brothers reunite at a designated meeting place, they compare gifts. However, when Ali peers through his ivory tube, he sees a most unwelcome sight: the princess is on her deathbed in their home kingdom far away, certain to die within a few days. Troubled, Hussein offers to transport them home on his carpet. When they arrive, Ahmed uses his apple to cure her immediately.
At first, everyone believes Ahmed should marry the princess, since his gift cured her. However, the Great Sultan rationalizes that each item was instrumental to her survival, so he devises an archery contest to decide the question. Ali wins the contest, and the wedding is held soon afterwards.
This story utilizes a trope quite common to folktales around the world, in which three brothers set out to find the most marvelous items they can, usually for the sake of a woman. In a larger sense, the trope of competition amongst brother resonates in folktales of almost every culture. Not every story in The Arabian Nights has clear equivalents in so many folk traditions, but this one is clearly tied to versions of stories told elsewhere in the world.
However, not all equivalents to this tale express such a positive theme as this one: cooperation. Though Ali ultimately wins the princess, the story overall suggests that we work better together than we do apart. Each brother found an item that he believed would set him apart, but they eventually save their beloved by using the items in conjunction.
(Admittedly, this message would have been a lot more potent had Prince Ali not ended up winning the princess anyway, but that says a lot about both their society and story audiences - it's almost unthinkable that the princess marry no one.)
This, of course, brings us to the princess's own role. As is most often the case with women in The Arabian Nights, the princess serves less as a person with agency than as an object to be desired. The only time she is almost included is when the Grand Sultan suggests she choose her own husband. Of course, the brothers immediately refuse this idea. Though the title character, Princess Nouronnihar never has her own voice in this story; she is merely the prize to be won, and then a challenge to be bested once she falls ill. Though she fares better than women in other stories, her position is yet another indication of how women were viewed during this time.
This story contains many of the elements that make The Arabian Nights notable. For one, it features a flying carpet, which many would associate with this world even without reading the work. The other magical items also evoke a mystical power. However, as is usually the case with these stories, the action comes through characters and human nature, rather than simply through magic. The items are instrumental to saving Nouronnihar's life, but would have been useless had the brothers not realized their cumulative value. As is often the case in The Arabian Nights, luck is important, but useless unless the characters capitalize on that luck.
One theme of this story that resonates with other stories is that of curiosity and skepticism. In addition, it adds another message: things are not always what they seem. All three items appeared to be dull and overpriced, and yet all three items ended up saving a person's life. There was more to the carpet, the tube, and the apple than met the eye. Had the princes not been curious men, they never would have asked after those items. (Of course, they also employ a skepticism that characters in many other tales do not. While other characters - like King Yunan, for instance - are too swayed by gullibility, the princes demand proof, thus evidencing their capable natures.) Too often we overlook what may be right in front of our eyes, and likewise, do not inquire enough to learn that what seems ordinary might have extraordinary potential.