Where "The Masterpiece Society" was the sort of talky story that I think is fairly specific to Star Trek (albeit not a good one), "Conundrum" is more general popular sci-fi fare (though it's definitely a subgenre of Trek as well). The premise, let's face it, is completely implausible. The entire crew of the ship has their memories blocked, and all evidence of who they are and why they're on the ship has been erased from the computer. Meanwhile, a mysterious new crew member, Commander MacDuff (Erich Anderson), has been suddenly inserted into the crew with the agenda of waging war against his bitter enemies. Via falsified information, he manipulates the Enterprise crew into pursuing this agenda.
That MacDuff is capable of such an elaborate ruse (including selective memory erasure, and wiping clean all related records from the Enterprise computer) and yet still needs the Enterprise and its crew as a weapon against his enemies is pretty hard to swallow. But sometimes TNG must be viewed as a laboratory/playground for strange and logically dubious things, and "Conundrum" is entertaining enough for me to forgive its unlikelihood. As a mystery, it finds its fun in the what and the why, even though the who is provided to us from the very first scene. It's more about the crew, rather than us, figuring things out.
"Conundrum" is also in the long-standing tradition of Trek stories that allow the characters to step outside themselves and essentially become someone else (in this case, blank slates that retain their original personalities, which become magnified by the situation). This is good for some low-key humor, particularly Worf's presumption that he may be in command of the ship. He sits in the captain's chair and tests the phasers (firing them into the void of space like a kid with a new toy), and then takes over Picard's ready room. Picard takes this all in stride, which is also funny to watch; always so unflappable and understanding, this man.
Meanwhile, Ro aggressively puts the moves on Riker, who voices no objections. Riker is also receptive when Troi reveals that she has discovered they had a romantic past. Riker gamely plays the part of a cheerfully likable womanizer (who gets his comeuppance in an amusingly played final scene). Hey, it's not his fault he's so awesome!
The plot resolves itself because the crew, despite having their identities erased, pretty much act as level-headed as they always would, asking themselves questions rather than launching mindlessly into action. Also, MacDuff does a pretty good job of stupidly blowing his cover. For a guy able to pull off such a deception, he sure hasn't done his homework about what makes these people tick. Hey, this isn't a great episode of TNG, but it's a fun one.
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