There was a cheat? I never got past that pesky arrow.

I don't even consider this a puzzle, but I want to mention a puzzle from an old Garfield fan adventure. There was a puzzle where you had to assemble a pipe system while the water was already coming. When ever you'd placed a piece, you were given another. It was a race against time.
After a while it switched from thick pipes to thin ones, because the first connection required a thick pipe, and the last connection required thin pipes.
The shape of the pipe pieces was randomized, and you just kept getting the thick parts until the game finally switched, usually so late that you didn't have enough room left to place them.
if you failed, you had to start over, but if you'd already reached the thin pipes, you just kept getting those, no thick ones.

I've never finished that game because I gave up eventually. It was just impossible for me.

Frustration level... 1000%!

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When I think of absurdity Curse of Enchantia comes to mind. There is this ONE puzzle that an Inuit that is fishing always faints when you appear on screen, you have to ASSUME that you smell bad and that's why he faints. So get this : you have to WEAR deodorant one screen prior to the Inuit so that he does not faint. I actually solved this out of luck in my Amiga 500 without realizing why, but when I read the walkthrough in a magazine my brain melted. 1992, without internet and the creators are feeling sadistic or a bit looney (too many cartoons). Jesus... still liked the game though

Perhaps the developers just assumed all teenage Adventure Game players smelled bad?
I mean... it's not a bad call 

This got me laughing 

The sliding puzzle in the church in Black Mirror 1. 

Ugh, god, that puzzle almost made me quit the game all together... Slider puzzles should be banned from adventure games!

I just remembered another one. The Feeble Files has several timed puzzles, which drove me crazy, but I'm persistant and managed to get through them eventually. The worst puzzle is in the arcade where you have to play Simon the Sorcerer arcade games for tokens to use elsewhere. The games are randomized but generally go from easy to impossible. The amount of tokens you win increases as well, but if you miss one, you forfeit everything. I learned very early to only try the first 3 games for 5, 20 and 100 credits. It’s a frustrating way to earn the 500 or so credits you need.