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Having failed to locate heiress Judy Jones, the law firm of Minland, Mahoney and Krencher decide to advertise. One of the many people who sees the ad is band leader Tommy Coles, whose girl friend, an addlepated singer, is named Judy Jones. Tommy has proposed many times to Judy, but she refuses to marry him until they have more money. After Judy makes a comment about her rich uncle Jonas Jones, Tommy realizes that she is really the missing heiress. By showing the lawyers a shrunken head that Jonas left to her, Judy proves her claim to his ten million dollars, but in order to inherit, she must marry a man with an I.Q. of 150 by a certain date. Using a man's name, Judy enrolls in an all-male school for geniuses. Her ruse is quickly discovered, but because she is attractive, and because she offers to pay for a new chemistry laboratory with part of her inheritance, professor Gabriel Popik allows her to stay in school. Younger professor Bartholomew Williams is not as susceptible to Judy's charms, however, and insists that she leave the campus. A horrified Popik demands that Williams beg Judy to return, but thanks to taxi driver Camille, she has already taken a waitress job at the campus coffee shop and refuses. After Judy accidentally serves Williams a sandwich made with a bar of soap, he angrily tells her that she epitomizes everything he hates about women. Tommy, who is also in the coffee shop, tries to defend Judy, but Williams knocks him unconscious, impressing Judy with his virility. Because Popik knows that Judy must marry a man with a high I.Q., he convinces Williams to romance her until she agrees to return to school. A few days later, Popik is sure that the stormy relationship between Judy and Williams is a sign that they love each other. When Judy joins Tommy and his band at a lakeside resort the night before her marriage deadline, Popik conspires with the lawyers, who are also at the resort, to bring Judy and Williams together. While the lawyers row Judy out to the middle of the lake, Popik brings a drunken Williams to the lakeshore. The lawyers overturn the boat and Williams swims out to rescue Judy. He confesses that he loves her, and she accepts his marriage proposal, to the dismay of Tommy and Camille, who loves Williams. Judy and Williams, together with the lawyers, Tommy, Camille and Popik, hurry to Nevada to be married. On the way, the police stop them for speeding and take them to jail. In their defense, Tommy reels off a lot of legal terminology and is forced to admit that he is a law school graduate and a former quiz kid. After Williams reveals that he has a low I.Q., but has worked hard to succeed, Tommy proposes again to Judy, whom he truly loves, and Camille proposes to Williams. The marriage plans are again interrupted when the wedding party is stopped by a convoy of returning soldiers, but everything is happily resolved when the army chaplain unites the two couples.