How to pitch Warren Buffett in 60 seconds or less

At the world’s richest business plan competition, more than 40 teams delivered a minute-long appeal to an imaginary Oracle of Omaha. Here are our favorites.

FORTUNE — In front of a standing-room-only crowd at a Rice University auditorium Thursday night, business plan contestants set the scene: A would-be student entrepreneur walks into an elevator with Warren Buffett. They have 30 floors — or 60 seconds — to get him to invest in their company.

More than 40 student teams delivered elevator pitches to an imaginary Oracle of Omaha. But the crowd was real: Nearly 500 students, investors, and Texas business leaders crowded into the Houston business school auditorium. This micro-spiel showdown is a high-drama event at the university’s annual business plan competition, which draws teams from all over the country to compete for $1.6 million over the course of three PowerPoint-filled days. Some stumbled — a few presenters went cold in front of the crowd. And some succeeded, you can see all the pitches here.

The judges will hand out prizes to the winning teams at a gala on Saturday night, including $1,000 for the best elevator pitch and $450,000 for the top team. But for now, Fortune has picked a few of its favorites.

Best appeal to the hypochondriac in all of us: NanDio, University of Notre Dame

The plan: The team says it has a simple diagnostic test for the human papillomavirus, which it says is causing epidemic levels of oral cancer, according to the Centers for Disease Control and Prevention.

The pitch: “Do you know what’s in your mouth? It could be HPV.”

Most likely to further depress manufacturing workers: NVBOTS, Massachusetts Institute of Technology

The plan: With 3-D printers already increasing the amount of automation in manufacturing, this team has developed one that can run all day and night.

The pitch: “We’ve eliminated the human from every step of the 3-D printing process. You can run our machines 24/7 without any human interaction.”

Most likely to spark a sequel to The Graduate: PolyDrop, University of Washington

The plan: The company wants to make durable plastic materials that can conduct electricity. The team thinks its semiconducting polymers could take over the electrostatic charge dissipation market (yes, it’s a mouthful), which it says is worth $2.3 billion.

The pitch: “We are PolyDrop, and we are completing the plastics revolution.”

Most likely to purge Britney Spears songs from your bar night:

CrowdTunes, Duke University

The plan: Create a digital jukebox marketplace where bar-goers can use their phones to control the sound system, paying per play, and paying more to play a song immediately.

The pitch: “Patrons can bid on their songs, and then outbid their friends with terrible taste. We’ve created a music marketplace where I’ve seen songs sold for $20 in bars.”

Best reason to ditch that arts career and get an MBA: FilmShaker, London Business School

The plan: FilmShaker promises to be the “Netflix of independent films.” With even the best indie films getting little distribution, the business would give those movies a platform, and a business model.

The pitch: “A few years ago, I met a producer whose movie won the Cannes Film Festival. He told me his movie hadn’t made any money.”

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