On Saturday, the Defense Advance Research Projects Agency set out to learn how quickly people could use online social networks to solve a problem of national scope.

The answer: eight hours and 56 minutes, at least when the problem involves $40,000 and a bunch of red balloons.

In DARPA’s Network Challenge, tied to the 40th anniversary of the Internet, the Department of Defense’s research arm placed 10 weather balloons in public places around the country. The first team to locate and submit the balloons’ correct geographic coordinates would get the cash prize. Ready, set, Twitter.

More than 4,000 teams participated. More than a few interesting things were revealed about the human psyche.

“It’s a huge game theory simulation,” said Norman Whitaker of DARPA’s Transformational Convergence Technology Office. The only way to win the hunt was to find the location of every balloon, but a savvy participant would withhold his sighting until he’d amassed the other nine locations, or disseminate false information to throw others off the trail.

Over the weekend, Twitter and Facebook were abuzz with offers to sell coordinates of alleged sightings. There was much excitement over the red balloon in Providence, R.I. But there was no red balloon in Providence — just a Photoshopped decoy circulated by a conniving player.

The winning team was spearheaded by Riley Crane, a postdoctoral research fellow at the Massachusetts Institute of Technology’s Media Lab. MIT’s team set up an elaborate information-gathering pyramid. Each balloon was allotted $4,000.

The first person to spot one would be awarded $2,000, while the people who referred them to the team would get smaller amounts based on where they fell on the information chain. Any leftover money, after payment to spotters and their friends, will be donated to charity.

Crane said the team’s decision to spread the wealth was instrumental to their success, as it gave people an incentive to share good information, and a feeling of investment in the process. He was less interested in the monetary prize than in the potential for social research.

“On the science side, we’re scratching the surface of this tremendous new system” of social networks, he said. “With this data set we have the potential to understand how to face — and exploit — the challenges that come with living in this interconnected world.”

The practical possibilities of the Network Challenge go far beyond a research lab. Already the powers of social networks are well documented: Earlier this year, information about violence in Iran continued to be dispersed through Twitter even after traditional news sources were squelched.

Crane wonders what types of applications might result from data about information dispersal collected this weekend: “Could we design an alert system to help us find missing children? Could we redesign the incentive structure for police rewards?”

DARPA officials plan to meet with participants throughout the week discuss their strategies.

Cities above which the balloons flew were Portland, Ore.; San Francisco; Santa Barbara, Calif.; Scottsdale, Ariz.; Katy, Texas; Memphis; Atlanta; Miami; Charlottesville, Va.; and Christiana, Del., according to DARPA.