Here's a breakdown:
* The Problem: Irene Adler, a renowned opera singer and former lover of King of Bohemia, possesses a compromising photograph that threatens to ruin the king's upcoming marriage. The king hires Sherlock Holmes to retrieve the photograph.
* Holmes's Plan: Holmes devises a complex plan to outwit Irene Adler. He pretends to be injured and arranges for Watson to be taken to a nearby hospital. Then, Holmes, disguised as a clergyman, visits Adler's house with a fake story of a dying man's wish to see her. Adler falls for the ruse and shows Holmes the photograph. Holmes switches it with a replica he has prepared.
* The Outcome: Irene Adler, a clever and resourceful woman, sees through Holmes's deception but chooses not to reveal his scheme. She gives him the original photograph and a note, saying "This is for the king," hinting that she will not use the picture to blackmail the king.
* The Resolution: Holmes retrieves the photograph, saving the king's reputation and allowing him to marry. The story ends with Irene Adler disappearing, leaving Holmes with a profound respect for her intelligence and her power.
The solution lies not only in the successful retrieval of the photograph but also in the acknowledgement of Irene Adler's wit and resourcefulness. This makes "A Scandal in Bohemia" more than just a simple detective story; it explores themes of love, power, and respect.