The Kobayasha Maru test is a no-win scenario simulation. But you can get a partial victory. Essentially how the cadet responds is used to try to figure out what kind of officer they would be.
There is variants as it changes with whoever the Federation's Cold War enemy is currently (there's always at least one).
Cold War bad guy ship(s) is threatening an innocent civilian ship in an area of space where the Federation is not technically allowed. Also the bad guys greatly outclass the ship.
You can preserve the treaty and your ship (and the lives of you and your crew) and let the civilians or you can sacrifice your ship and the treaty to save the civilians.
Technically cadets are not supposed to know they are playing an unwinnable scenario until after they try it once, but leaks happen. Captain Kirk found out about it and made a plan.
In both Star Trek universes, Captain Kirk won the unwinnable scenario by cheating.
The closest anyone came to winning without cheating was Nog in the expanded universe. Nog lost the first time, and like many cadets wanted to try it again. The second time, he approached it like a Ferengi and attempted negotiations with the attackers. The negotiations got complex and the program was built around military lines and the program crashed.
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