> Another on that really irritates me is the kind that presents a series of integers and asks which integer comes next. Any integer will do, you just have to fit the appropriate polynomial.

This one bugs me to no end because it's part of the standard elementary school curriculum, for example here: https://byjus.com/maths/patterns-questions/

But surely someone with a strong imagination could come up with a pattern to fit any number as the next in the sequence. I doubt most elementary educators even grasp the issue.