Rahul Nagvekar, a 14-year-old from Texas, is congratulated by host Alex Trebek at the 2012 National Geographic Bee. (Sarah L. Voisin/WASHINGTON POST)

Ten students from across the country gathered in downtown Washington Thursday morning for the 24th annual National Geographic Bee. For two harrowing hours, they answered geography questions, analyzed world maps and climate charts, and fielded personal questions from the host, Alex Trebek of “Jeopardy” fame.

One after another, the competitors with the fewest points were eliminated until just two finalists remained, facing off over this question: What Bavarian city on the Danube River served as the legislative seat of the Holy Roman Empire from 1663 to 1806?

Audience members glanced around in confusion — Bavarian what? Holy Roman Empire? — as Trebek repeated the question. The 12-second time limit ticked down. Rahul Nagvekar, 14, of Texas and Vansh Jain, 13, of Wisconsin huddled over their monitors and scribbled their answers. At stake: a $25,000 college scholarship and a trip to the Galapagos Islands.

“Been there, done that — a fabulous vacation,” Trebek quipped.

Finally, their answers were locked in. Jain wrote Passau. Nagvekar went with Regensburg. He was right.

Adam Rusak, a 13-year-old from Gaithersburg, was among the 10 finalists at the contest. (Sarah L. Voisin/WASHINGTON POST)

“It was a complete guess,” Nagvekar said later. “I was thinking of two cities, Regensburg and Ingolstadt. Luckily, Regensburg was correct.”

If this question seems obscure, it’s not your imagination. The questions at Thursday’s bee presented geography puzzles in the context of world history, culture and current events. President Obama even appeared via video, asking students which Asian city on the Han River hosted the nuclear security summit in March. (The answer was Seoul.)

The questions were the last step of a months-long process to whittle down a pool of thousands of students from each state, the District and the U.S. territories. In the end, 10 finalists competed for their share of more than $50,000 in prizes.

While Nagvekar won the the grand prize, runnerup Jain and third-place finisher Varun Mahadevan, 13, of California got $15,000 and $10,000 scholarships, respectively. In fourth place, Raghav Ranga, 14, of Arizona took home $1,000.

Adam Rusak, an eighth-grader at Lakelands Park Middle School in Gaithersburg, was among the finalists. Trebek was impressed by Rusak’s interest in coin collecting and crossword puzzles, which he does in English and Polish. But the 13-year-old was the first to be eliminated.

“I want you to take some solace in the fact that you made it here to the top 10,” Trebek told him.

Rounding out the top 10 were Karthik Karnik, 14, of Massachusetts; Gopi Ramanathan, 14, of Minnesota; Anthony Cheng, 13, of Utah; Anthony Stoner, 14, of Louisiana; and Neelam Sandhu, 13, of New Hampshire.

With each incorrect answer, the teenagers fought to maintain their composure. Emotions ranged from visible shock to audible disappointment to, finally, utter surprise.

Nagvekar said he had only two things on his mind during the course of the competition: to stay calm and survive through the final round.

“My goal was to be on the stage when the last question was read,” he said. “I wasn’t expecting to win.”

Several of Nagvekar’s competitors had ahistory with the bee. Karnik was a finalist in 2011, Stoner was a three-time state champion in Louisiana, and this was Jain’s third time competing in the finals. Sandhu, the only girl in the competition, said her older brother had competed in 2008, when he came in fifth.

“There were people on stage that had won state three or four times and had perfect scores at prelims on Tuesday,” Nagvekar said. “I didn’t have that.”

What he lacked in competitive experience, Nagvekar made up for in discipline. “I’ve been preparing since I was in the fourth grade,” he said. “I’ve gone through a lot of maps.”