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The Kobayashi Maru is a fictional fuel carrier-ship in the fictional Star Trek universe which serves as the basis of a scenario for cadet training at Starfleet Academy.
In the 2280's Kobayashi Maru scenario, the Kobayashi Maru strikes a mine in the Organian Neutral Zone. The captain of another starship is then faced with the dilemma of:
Regardless of the option taken, a cloaked Klingon ship attacks and destroys the would-be rescue ship. The purpose of the scenario is to evaluate the cadet's behavior and thought process in a no-win situation. As a consequence, the term Kobayashi Maru problem has entered common parlance to describe a test designed solely to determine some usually non-tangible human thought process. See also: Fermi problem
The only cadet to ever win that version of the scenario is James T. Kirk, who reprogrammed the simulation. When he hailed the simulated Klingon ships, giving his name as "Captain James T. Kirk", the Klingons had been programmed to reply "The James T. Kirk?" In the revised simulation, James T. Kirk was a famous captain that no Klingon would dare to take on. He justified it by arguing that a no-win situation was cheating, and so he had to cheat in return.
With the alliance between the Klingons and the Federation, it's unclear what shape the Kobayashi Maru scenario had taken by the Star Trek: The Next Generation era.