In the isolation booth, Herb Stempel bit his lip to show tension. He dabbed sweat from his brow and sighed into the microphone. And as 50 million viewers hung in suspense, he seemed to agonize over the question in his last appearance on the rigged NBC quiz show “Twenty-One.” What movie won the Academy Award for best picture in 1955? It was Dec. 5, 1956, and Mr. Stempel, a City College student from Queens, was in his eighth week on the show, posing as a nerdy know-it-all. He had won $49,500. But his new rival was Charles Van Doren, a...