Mrs. Frankweiler's driveway is remarkably long, almost like a highway in itself. It leads deep into the woods. Jamie remarks that the house looks like another museum. The children pay the taxi driver with the very last of their money. Parks, Mrs. Frankweiler’s butler, opens the door to the mansion. After stating that they are here to seek information about the Italian Renaissance, they are ushered into Mrs. Frankweiler's study, a vast place that resembles a laboratory.
Mrs. Frankweiler makes them wait several minutes before speaking. She asks if they are the children who ran away from Greenwich, Connecticut a week ago, and despite their great surprise, they confirm that they are. She invites them to sit down and discuss the Italian Renaissance. They end up discussing the newspaper article about their disappearance - the children critique and marvel at the photos of themselves in the paper.
Because the children are very dirty, Mrs. Frankweiler demands that they take a bath. Claudia luxuriates in the beautiful tub, but Jamie washes up quickly. He sits down at the dinner table with Mrs. Frankweiler, and comments that they should start eating without her - Claudia loves baths, and even made them both bathe at the Metropolitan Museum of Art. He hesitates when he realizes he's given away their secret. Mrs. Frankweiler is intrigued about how they managed this feat, but Jamie says that she has to ask Claudia. Jamie also reveals that the two children are broke, which explains why they can't just leave Mrs. Frankweiler's mansion.
Jamie also challenges Mrs. Frankweiler to a game of cards, though he confesses that he does cheat. They start eating lunch.
Claudia is a bit annoyed when she finally emerges from the bath, but she is intrigued when Mrs. Frankweiler's butler says that the next course is ‘Nouilles et fromage en casserole’. However, this turns out to be just macaroni and cheese. Mrs. Frankweiler says that she is just a simple woman under all the fancy trappings, and everyone laughs.
Mrs. Frankweiler suggests that Claudia call her parents for a ride home, but she refuses - she wants to find out the truth about Angel. Mrs. Frankweiler asks if this is related to where the children have been all week, but Claudia refuses to answer. Suddenly, she realizes that Jamie has told Mrs. Frankweiler where they have been, and she angrily calls him a blabbermouth. Mrs. Frankweiler offers to give them a ride home in her Rolls Royce if they tell her about their adventures, but Claudia refuses, declaring that she just wants to know about Angel.
Mrs. Frankweiler escorts the children into her study. The room is lined with numerous filing cabinets. In one of them, says Mrs. Frankweiler, is the secret of Angel. However, the files are in an order that makes sense only to her; the children have one hour to find the file, but they must make sure that everything goes back in its proper order. Mrs. Frankweiler leaves the study, but stays just outside in order to listen to the children's discussions.
Jamie goes to open the file drawers immediately, but Claudia tells him to stop - they will create a plan first. She makes a list of terms related to the statue (sculptor, Florence, Italy, Michelangelo, Angel, marble, Metropolitan Museum of Art, etc.), and assigns half the terms to Jamie. However, none of the terms is correct.
Jamie uses the exclamation ‘oh baloney’, and this sparks an idea for Claudia: she looks under Bologna, Italy, where the statue was purchased. Sure enough, they find the file they were looking for. In the file, they find a poem in Italian and a sketch of Angel with Michelangelo's signature. The paper is very old. Claudia starts crying.
Mrs. Frankweiler returns. She claims she knew Michelangelo did the statue even before she got the sketch. Jamie asks where she got the sketch, and she explains that she won it in a poker game. She goes on to explain that she will give the sketch to the children if they tell her where they hid all week and how they did it. She'll make sure that they keep the sketch a secret because she won't give it to them outright, she will leave it to them in her will.
Mrs. Frankweiler notes that Jamie wants the sketch because it's worth a whole bunch of money, and Claudia wants the sketch because it's a secret that enables her to feel different and special. Mrs. Frankweiler wants to hear their story because she's a collector of rare and interesting things, and the tale of two children who hid out in a museum for a week qualifies as just that.
Claudia asks if Mrs. Frankweiler ought to give the sketch to the museum - after all, they are struggling to determine whether or not Michelangelo carved the sculpture. Mrs. Frankweiler says that this will just result in the authorities trying to determine the authenticity of the sketch, and though most will agree it's genuine, some will continue to argue against it. Claudia asks if she wouldn't want to know without a shadow of a doubt if the statue is genuine. Mrs. Frankweiler says that she is old and satisfied with her research on the subject; she has allowed the facts to rest and accumulate within her.
Mrs. Frankweiler comments that there is just one new thing she'd like to experience: she'd like to know how Claudia and Jamie's mother feels. She herself never had children.
Mrs. Frankweiler keeps the children up all night telling her the story of their time stowing away at the museum, which they do enthusiastically. At one point, the children's mother calls in a panic, and Mrs. Frankweiler assures her that she will return them safely in the morning. Mrs. Frankweiler comments that Saxonberg probably could not resist telling her, which raises the question once more of Saxonberg's particular relationship with the children.
In the morning, Mrs. Frankweiler's chaffer Sheldon drives the two children home in a Rolls Royce. Claudia and Jamie puzzle over why Mrs. Frankweiler sold the statue of Angel, which she knows was created by Michelangelo himself, to the museum for such a low price. Jamie figures that she wanted to share part of her secret - after all, it is no fun having a secret if no one knows you have it. The children also decide that they will visit Mrs. Frankweiler again when they have money - they will adopt her as their new grandmother. All of this information is relayed to Mrs. Frankweiler by her chaffer. Mrs. Frankweiler is amused and touched by this decision, and she tells Saxonberg that if he is their grandfather, she is not sure what this will mean for their relationship.
Mrs. Frankweiler notes that security at the Metropolitan Museum of Art has been tightened because of some strange discoveries amount the art objects: guards found a trumpet case and a violin case among the artifacts. They have been sent to the lost and found, but they have never been claimed.
Mrs. Frankweiler's personality is somewhat of a combination of Jamie's and Claudia's. She has Claudia's interest in fine things, as well as her intelligence and her impatience with things that irritate her. She also has Jamie's sense of humor and tendency to cheat at cards. Mrs. Frankweiler draws together the central traits of the two main characters, while also exhibiting all her own peculiarities.
Mrs. Frankweiler's somewhat paradoxical personality is illustrated by the nouilles et fromage en casserole, which is an important symbol as well as a dish. When the cook serves them nouilles et fromage en casserole, Claudia is delighted by the name of this dish, which sounds extravagant and French. She is surprised to discover that it is only macaroni and cheese. Mrs. Frankweiler explains that underneath all the fancy trappings (her mansion, chaffer, butler, marble sinks, and so on) she is really a very ordinary woman. The nouilles et fromage en casserole becomes a symbol of Mrs. Frankweiler's true nature: under all her fanciness, she is a no-nonsense woman.
At last, readers know where the strange title of the novel came from: Mrs. Frankweiler's files are indeed very mixed-up, and Claudia and Jamie work together to solve the mystery. Claudia carefully plans search terms and strategy, but it is the sudden revelation that Jamie's outburst sparks in her that enables the children to find the file they need. They could not have done it without each other.
Throughout the novel, Mrs. Frankweiler has addressed a number of remarks and observations to Saxonberg, her lawyer. However, why on earth would Saxonberg be interested in the story of two children who ran away to the Metropolitan Museum of Art? What is Saxonberg's relationship to the children? Finally solved: he is their grandfather. Here we have another long-standing question of the novel answered at last.
At the end of the novel, it is revealed that the children have left their instrument cases, containing all their clothes and possessions, in the museum. They've even left Jamie's transistor radio, which had previously been one of their most treasured possessions. The bags are brought to lost and found, but no one ever claims them. The bags are a symbol for all of the emotional baggage that Jamie and Claudia have shed during the course of their adventure. What seemed so important to them before now seems meaningless, because they have found greater treasure.