ARLINGTON, Va. — The Defense Advanced Research Projects Agency is different from other federal agencies. For one thing, the agency, known as Darpa, created the Internet (really). For another, it is probably the only agency ever to offer a $40,000 prize for a balloon hunt, a contest that was inspired by Regina Dugan, a 47-year-old expert in mine detection, who took over last summer as its director.

Dr. Dugan, who has a Ph.D. in mechanical engineering from the California Institute of Technology, is the first woman to be the director of Darpa, and those who know her say she has a knack for inspiring, and indeed insisting on, creative thinking.

Last December’s balloon hunt, otherwise known as the Darpa Network Challenge, is a good example. In marking the 40th anniversary of the connecting of the first four nodes of the Internet in 1969, the agency offered a $40,000 prize to the first team of volunteers able to locate 10 large red balloons hidden around the country.

The task only sounds frivolous. It was actually something that experts agreed was impossible using traditional intelligence techniques. The challenge was designed to test new methods, involving the use of social networks.