The BBC series Sherlock episode featuring the three-gunmen puzzle is “The Great Game.” It is the third and final episode of the show’s first series, broadcast in 2010.
The episode presents Sherlock with a sequence of cases sent by Jim Moriarty, who threatens to kill innocent people unless Sherlock solves each mystery. The three-gunmen puzzle is part of a hostage situation involving a kidnapped security guard and a hidden message. The structure allows the episode to move rapidly between seemingly unrelated investigations while building toward Sherlock’s confrontation with Moriarty.
“The Great Game” is also important because it develops Moriarty from a mysterious criminal organizer into Sherlock’s principal adversary. Its final scene takes place at a swimming pool, but the episode’s title and puzzle structure distinguish it from the separate episodes that continue the rivalry. Mark Gatiss wrote the episode.