By Anne Fisher
April 4, 2012

FORTUNE — Let’s say you’re one of a roomful of people, none of whom have ever met each other before, and someone asks the group to line up according to birthdays, from January 1 to December 31 — without talking. How would you manage that?

This is one of the tasks professor Tina Seelig gives students in a course on creativity and innovation she has taught for the past 12 years at the Hasso Plattner Institute of Design (known as the “D-school”) at Stanford University. Seelig is also executive director of the Stanford Technology Ventures Program.

In her new book, inGenius: A Crash Course in Creativity, she describes how students usually approach the problem — most often by using some kind of improvised sign language, which rarely gets people lined up in the right order.

A few of the far more effective solutions that no one thinks to try: Writing everyone’s birthday on a sheet of paper (no talking doesn’t mean no writing) and organizing the line accordingly; or having everyone pull out their driver’s licenses and then lining people up by the dates printed there; or drawing a timeline on the floor and having everybody stand on it.

“The results of this simple exercise are surprisingly predictable across ages and cultures…. Unfortunately, most people are satisfied with the first solution they find,” Selig writes, which “very often leads to predictable and mediocre results.”

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That’s in spite of the fact that, Seelig insists, the knack for finding better (even brilliant) solutions is hardwired in humans. “Nobel Prize-winning neuroscientist Eric Kandel says that the brain is a creativity machine, designed for problem-solving,” she notes, adding that the word “ingenious” is derived from the Latin ingenium, which means natural ability or innate talent.

So why do so many companies find innovation such a struggle? A big part of the answer is that trying to create something truly new means generating lots and lots of ideas, with the understanding that most of them are going to be flops. Few businesses are prepared to tolerate, much less encourage, the inevitable failures.

Facebook is, apparently. Top management knows that “on average, about one-third of all projects they attempt will work out,” Seelig writes. “That means that, in order to get four successes, they need to do a dozen experiments.” Facebook’s monthly 12-hour “hack-a-thons,” where employees are encouraged to spend a night brainstorming new projects, have produced thousands of silly, impractical, unmarketable ideas — but also some good ones, like Facebook Chat.

inGenius is a fascinating blueprint for any company that’s serious about creating an environment where new ideas can thrive, and many of Seelig’s students doubtless go on to do precisely that. But in the vast majority of workplaces (unlike in, say, a classroom, where the biggest possible downside is a lousy grade), failed experiments are just too risky.

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