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At the San Francisco airport baggage claim, mysterious Mr. Smith retrieves his plaid overnight case containing secret documents and proceeds to the Bristol Hotel, stalked by the furtive Mr. Jones. Also traveling from the airport to the Bristol is absent-minded Howard Bannister, a music professor from Ames, Iowa who is attending a musicology convention and carrying a plaid case similar to Smith's, although Howard's case contains pre-Paleozoic igneous rocks crucial to his research project. With Howard is his domineering fiancée, Eunice Burns, who manages his life but, concerned about "propriety," plans to check into a separate hotel room. During their cab ride to the hotel, their cab and several cars almost hit Judy Maxwell, a starving college student carrying a plaid case, who is following a pizza delivery man. Also checking in at the hotel is wealthy Mrs. Van Hoskins, whose plaid case filled with jewelry is coveted by two thieves, the hotel clerk, Fritz, and house detective, Harry. Sent by Eunice to the drugstore to buy some aspirin, Howard is distracted by a souvenir rock when Judy, chomping on a carrot stolen from the tray of a passing waiter, approaches him and flirtatiously asks, "What's up, Doc?" As she talks knowingly about geology, Howard tries to escape from her advances, but knocks over a display and when Judy tries to grab his jacket, it accidentally rips. When Eunice arrives, Judy upsets her by mischievously pretending to be Howard's castoff paramour. Later, Judy goes to room 1717, planning to stay without paying, but, seeing Jones inside, instead enters 1716, which is open. Finding Howard's jacket there, she mends it, stashes her overnight case in his room and sees an invitation to a banquet. In the hallway, Jones spots Mrs. Van Hoskins' case, which he presumes is Smith's, and later breaks into her room and takes her case. In room 1714, Eunice prompts Howard on how to present himself to Frederick Larrabee, the philanthropist offering a twenty thousand dollar research grant. As Eunice is not ready, Howard proceeds to the banquet alone, fumbles his introduction to Larrabee and meets his rival for the grant, the arrogant Hugh Simon. Sitting at Howard's table is Judy, who, posing as Eunice, is bewitching Larrabee and other musicologists with her wit, sex appeal and extensive knowledge. She manipulates the conversation to allow tongue-tied Howard to explain his theory that early man played crude melodies on rocks and elaborate his research, which involves the testing of rocks for inherent tonal qualities. Upstairs, Jones finds he cannot leave without being seen and Smith, thinking Jones is still after the documents, breaks into Mrs. Van Hoskins' room and hides his suitcase there. Afterward, Harry breaks into her room to steal her jewels and unwittingly takes Smith's case. Harry then hides in Eunice's room and stashes the case under her bed, unaware that Howard's case is there as well. Downstairs, the desk attendant refuses to let the distressed Eunice join the banquet because her name tag, which has been stolen by Judy, is missing. Although Howard repeatedly denies that Judy is his fiancée, Larrabee says her presence has increased his chance of winning. When Eunice forces her way into the ballroom, begging hysterically that Howard identify her, he claims not to know her, but is ashamed afterward. Fritz goes to Eunice's room and, unaware that there are two suitcases, grabs one, but then must slip it into Mrs. Van Hoskins' room to avoid being seen with it. After the banquet, Howard finds that Eunice left what she thinks is his suitcase outside his door. Inside his room is Judy, taking a bubble bath. When Eunice demands to come in, Howard convinces Judy, wrapped in a towel, to wait on the window ledge. Meanwhile, Harry enters Mrs. Van Hoskins' room and steals the case, but Smith presumes Jones has taken it when he sees his nemesis exiting through the hall window and walking along the ledge. As Eunice and Howard quarrel, Judy stumbles over the ledge, to which she hangs by her fingertips, and Howard accidentally causes a fire. Startled by Judy, Jones crashes through the window into Howard's room. Fritz and the firemen arrive, alerted by the smoke. During the pandemonium, no one notices Smith take Judy's case from Howard's room. The next morning, Howard is evicted, but the elevator takes him up instead of down, letting him off at a restaurant under renovation. Playing a piano, he awakens Judy, who is sleeping under a tarp. She sings, advancing seductively, until they fall off the bench. Half-heartedly evading her overtures, Howard asks about her wide knowledge. Judy says her father, determined to educate her, sent her to several universities, where she excelled in a variety of majors but was expelled from every one for the catastrophes she caused. Judy then gives Howard a letter from Larrabee, which states that he won the grant. Despite his attraction to Judy, Howard invites Eunice to the reception in his honor at Larrabee's mansion, where he promises to introduce her as his true fiancée. As she is not dressed, Eunice says she will meet him there. Smith sees Howard carrying a case similar to his and, looking inside the one he possesses, finds Judy's clothes. Determined to switch bags, he follows Howard. In the lobby, Judy overhears Fritz tell Harry to deliver the jewels to a certain address and calls Eunice's room and, pretending to be Larrabee's secretary, directs her to the address she overheard. Fritz and Jones see Judy, Howard and Smith depart, all bearing plaid cases, and follow, leaving the lobby just before Mrs. Van Hoskins enters and announces that she has been robbed. Shortly afterward, Eunice is dropped off by her cabbie at an isolated building in a bad part of town and finds a gang of men beating Harry for delivering Howard's rocks instead of jewels. At Larrabee's art-filled mansion, when asked to demonstrate his rocks, Howard finds jewels in his case and documents in Judy's. Smith then enters, carrying a suitcase and demanding the documents, and Jones, carrying a gun, does the same. Abruptly, the gang enters with Howard's case and Eunice, demanding the jewels. A fight ensues, during which Howard and Judy grab all four cases and steal a delivery boy's bicycle. As they pedal up and down the hills of San Francisco, they are chased by Smith, Jones, Fritz and the gang, all of whom are driving cars. In the gangsters' car, the terrified Eunice introduces herself to her fellow captive, Larrabee. Judy and Howard take refuge in a Chinese parade and then a costume shop. They steal a car from a newly married couple exiting a church and race to Sausalito in hopes of catching the ferry before it departs. Just as they arrive, the ferry is pulling out of the dock, and when Judy depresses the gas peddle to catch it, their car falls into the bay, as do those of their pursuers, and all are arrested by the police. Everyone is taken to a courtroom, presided over by a cranky, hypochondriac judge eager to charge them with everything he can. At the judge's questioning, Jones explains that he is a government agent pursuing Smith, who stole secret documents, and Howard confuses the judge with his muddled explanation. When the judge orders the person who is hiding under a blanket to come forth, Judy uncovers herself, and says, "Hello Daddy!," revealing that she is his daughter. After all the suitcases are returned to their owners, Howard, stripped of the grant, goes alone to the airport, where Judy approaches him. Fearing more trouble, he rebuffs her. Before catching her plane, Mrs. Van Hoskins says that from the $20,000 reward she offered for the return of her jewels, she has paid the cost of the damages they caused. Larrabee and Eunice, who bonded during their ordeal, come to see Howard off, along with Simon, the new grant recipient. Encouraged by Judy, Simon talks about his research project, which she and Larrabee realize has been plagiarized from a little-known scholar's work, prompting Larrabee to award the grant back to Howard. On board, Howard discovers that Judy is traveling to Iowa to study musicology. He admits he loves her and apologizes for rejecting her, but she says, "Love means never having to say you're sorry." As they kiss, a cartoon being shown to the passengers ends with Porky Pig announcing, "that's all, folks."