The team has a single clue: a coded message left in a typewriter by a secret agent.
With 60 minutes ticking down on the large electronic wall clock, they must unravel dozens of codes, clues and leads to discover the keys that can stop the blast.
"Escape Room" the real-life adaptation of a classic 1980s videogame is a new craze popping up around the world.
Having already made its mark in London, Paris and Bangkok, games are being organised in some unlikely spots around central Europe, including the picturesque Danube city of Novi Sad in Serbia where it has reached the number three spot for "things to do" on travel website Trip Advisor.
"This is a complex game that requires ability, intelligence, education and team work, much more than the online version," said Boban Melkus, a 36-year-old high school teacher who set up the game in Novi Sad.
Melkus and his wife Nina began offering the game in December in a rented apartment. Teams pay 4,000 dinars (35 euros, $45) to play in one of two rooms that have been given a Cold War makeover.
'We saved the world'
There are old-fashioned telephones that act as "hotlines" to Berlin, Madrid, Athens; a decades-old typewriter, and walls plastered with military maps and photos of Cold War-era leaders.
The business was profitable from the very first day, even though they only put a small ad on their Facebook page, said Melkus.
"We have two rooms: players can save the world from a nuclear catastrophe or rob a bank," Melkus explains.
He says players can get their money back if they are not satisfied, but "so far, nobody has asked for it. We even had a team from a computer games company, but it was difficult for them and they only just saved the world," joked Nina.
It attracts all ages from 15 to 60 but fans of the former computer game in their 30s and 40s are the most common, she added.
Zorica Ljubicic, a 53-year old clerk who had no experience with the virtual version, came out beaming with satisfaction after she and two friends averted the apocalypse.
"This was such good fun everything was so exciting, we saved the world!"
Her friend Zarko said their team skills were key to their success.
"Next we will rob a bank," she said.
The Melkus couple first played it in Budapest in Hungary, where it has seriously caught on, with over 40 companies organising the game in more than 100 rooms around the city.
The couple plans to take the game next to the Serbian capital Belgrade, as well as Geneva and Zurich in Switzerland.
It's become a popular team-building event for businesses in contrast to the original version of the game which was a purely solo affair.
"Here, you are nothing without a team," Nina said.
Building on this part of the business, the Meldeks have even engaged the services of a psychologist to make a profile of each player based on their response to the puzzle.