[TOS] Season 3, Episode 14: Whom Gods Destroy
This episode is fun and I like that the problem Spock has to solve at the end exemplifies the characters in a cool way, even if the situation itself is kind of cliched and silly.
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Read more at Memory Alpha
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Notes:

Kirk and Spock beam to a facility where people are kept with mental issues. The building is surrounding by a shield and is on a planet where all the air is poisonous.

But then they’re fooled by a crazy guy named Garth. He somehow learned to morph into whatever he wants. It was a little trick he picked up while visiting some aliens.

He is in control of the facility with his friends. Garth used to be one of Starfleet’s most respected captains, and one of Kirk’s heroes

He eventually figures it out because one of them suggests Spock just shoot both of them and then sort it out
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