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Beauregard Bottomley, a reserved intellectual with a number of academic degrees but no marketable skills, shares a Los Angeles bungalow with his sister Gwenn, a piano teacher, and their dipsomaniac parrot, Caesar.  On their way to the movies one night, Beauregard and Gwenn stop at a television display in a store window, around which people have gathered to watch a quiz show called Masquerade for Money, in which contestants dress up as their favorite person or thing, and then answer questions about that person or thing.  The show's host, Happy Hogan, pays the contestants for each correct answer, doubling the prize to a maximum of $160.  Beauregard is aghast at both the program and its cheerfully vapid host, perceiving them as a threat to the country's intellectual standards.

The next day, the clerk at the state employment office sends Beauregard to apply for a research job at the Milady Soap Company, which makes "the soap that sanctifies" and sponsors Masquerade for Money .  Beauregard's interview with eccentric president Burnbridge Waters takes a bad turn when Beauregard makes a small joke, and the job offer is withdrawn.  Determined to get revenge, Beauregard appears as a contestant on the show, wearing an encyclopedia costume.  Prepared to answer questions on any subject, Beauregard's caustic wit makes him popular with the studio audience.

After winning $160, Beauregard stuns Happy and the Milady executives by refusing to take the money, insisting instead on coming back next week to play for double or nothing.  Sensing a promotional opportunity, Burnbridge decides to keep Beauregard on the show for a while, and both the ratings and the company's sales soar.  With Beauregard's winnings now at $40,000, Gwenn urges her brother to take the money, but he refuses, explaining that he plans to keep playing until the prize matches the value of Milady, or $40 million, at which point he will take control of the company and pull the quiz show off the air.  When Beauregard wins again, Burnbridge and his executives resolve to defeat him, and Happy volunteers to sign up for piano lessons with Gwenn.  Although she suspects his ulterior motives, Gwenn begins to date Happy, and they fall in love.

When the prize money reaches $10 million, Burnbridge enlists the help of the alluring Flame O'Neil.  Dressed as a nurse, Flame goes to Beauegard's home, where he is in bed with a cold, and introduces herself as a "present" from his fan club.  Beauregard soon falls in love with her, which leaves him somewhat addled, and Flame further manipulates him by making him think she is seeing another man.  Beauregard tells Flame that his one area of weakness is Einstein's space-time continuum, and that night, a question on the show is about that very subject.  The judges rule his answer incorrect, but Einstein calls from Princeton to tell Happy that Beauregard is right.  Beauregard goes to Flame's apartment and spanks her with a hairbrush, and after he admits that he deliberately misinformed her to confirm his suspicions, they kiss.

Meanwhile, Burnbridge decides to go out of business in style, and he books the Hollywood Bowl for what could be the final show.  Gwenn announces her engagement to Happy, and Beauregard announces his to Flame, but they are both uneasy about the fact that Happy and Flame insist on waiting until after that night's broadcast to marry.  When the big moment arrives, Happy takes Beauregard's wallet and asks him to recite his Social Security number.  To everyone's horror, Beauregard's answer is wrong.

Later that night, Burnbridge shows up at the Bottomley residence with a case of champagne and is immediately recognized by Caesar, who was his pet in college.  While Burnbridge and his parrot enjoy their reunion, Happy arrives, followed by Flame.  As Beauregard and Flame drive to Las Vegas to get married, he tells her that he had made a deal with Burnbridge to lose the last show, which was fortunate for him, because he really did not know his Social Security number.  When Flame sees a number of books in the backseat, which Beauregard intends to read on the honeymoon, she laughs as she tosses them out of the car.