Kobayashi Maru
From Hidden Frontier
The Kobayashi Maru scenario is the infamous no-win scenario that is part of the curriculum for command-track cadets at Starfleet Academy. It is used to assess a cadet's discipline, character, and command capabilities when facing an impossible situation.
In the version of the scenario employed in the 2280's, a cadet was placed in command of a starship on patrol near the old Klingon Neutral Zone. The starship would receive a distress signal from the SS Kobayashi Maru, a civilian freighter that had been disabled in the zone after having struck a gravitic mine. If the cadet chose to enter the Neutral Zone in violation of treaty, the starship would be confronted by three Klingon battlecruisers. The test was considered a no-win scenario because it was considered impossible for the cadet to simultaneously save the Kobayashi Maru, avoid a fight with the Klingons, and escape from the Neutral Zone intact. (Star Trek II: The Wrath of Khan)
Based on Ensign Brad Rawlins' use of the distress call from this scenario, it would appear that some version of the Kobayashi Maru scenario is still used at the Academy as late as the 2370's. (HF 1.03 - "Enemy Unknown, Part 3")
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