Here's a summary of how they solve it:
* They notice patterns: Petra and Calder realize that the theft of a Vermeer painting from the museum isn't a random event. They notice that there's a connection between the painting and other recent events, including the appearance of mysterious coded messages and the theft of a valuable antique compass.
* They decipher the codes: Using their knowledge of art history and a few clues, they figure out that the codes are based on the art and life of Vermeer. They decode the messages, which lead them to a hidden message within a Vermeer painting itself.
* They follow the clues: The messages lead them on a journey through the city, uncovering more clues and meeting people who can help them.
* They uncover the truth: Through their investigation, they discover that the thief is actually a museum curator who wants to use the Vermeer painting to prove a theory about the artist's secret life.
* They bring the culprit to justice: The children use their newfound knowledge to expose the curator's crime and help get the painting returned to the museum.
The novel emphasizes the power of observation, curiosity, and teamwork in solving mysteries.