Fast forward a decade and several jobs later, my favorite take-home so far is simply a no-nonsense assignment that reflected the actual work I would be doing. As a frontend person, that meant making a dashboard in React or whatever JS flavor I wanted, with whatever tools I wanted, for a co-review a few days later.
They asked me to make something like a movie browser, kinda like Netflix, using a provided list of 100 or so movie titles. It was a pretty simple project that only took a day or so, but showed enough basic React listing/filtering/searching/state/context usage, and some simple API lookups (used it to get cover/poster art and some metadata from IMDB). It wasn't a particularly challenging assignment, but it wasn't meant to be – it was just a normal frontend job at a traditional (non-tech) Fortune 1000 company.
After I submitted the assignment, the interviewer spent an hour or so walking through it with me, asking questions about certain parts and offering constructive feedback on others. It was a really good use of both of our time: them to see how I think through user-facing problems, and me to see how they like to manage work and communication.
I got the job, and did very well in it, and helped solve a few interesting challenges at that company (the dashboard was complex enough that it had interesting UX, IA, error handling, user flows, visualizations, etc.)
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One take-home I did NOT really like was from an online interactive mapping company I really respect. They asked me to make an animated analog stopwatch, similar to the kind you'd hold in your hands at a race. I'd never really done any animation before, and their product didn't seem to have much of it, but that was the assignment.
I made one and it worked, with some caveats. The assignment didn't have much detail to begin with, so I submitted what I had and told them I'd be happy to modify it or rewrite the whole thing to spec, in whatever stack they wanted. A few hours later they told me sorry, but no thanks, and that was that. No further feedback.
It annoyed me because the take-home didn't really seem to reflect any sort of work I'd actually be doing anyway (web dev + mapping), which I actually had a moderate amount of prior experience with. The GIS (geo information systems) world has plenty of its own nuances and interesting challenges, but none of that was tested or discussed at all. To this day I still don't know why they wanted an animation challenge for a web mapping app.
Presumably they cared more about the graphics side of things, or it was just a chance for the right candidate to write something really cool from the ground up to impress. The assignment itself was flexible enough that it could've been anything from "here's a npm lib that does this with a SVG" to "I wrote an entire 3D renderer with ray-tracing to better simulate the watch face". I did not impress :)
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Oh, and one more bad/ridiculous experience: One company's first "take-home" wasn't even a coding challenge, but some sort of convoluted personality test. They made you sign up for a third party platform to take a specific personality test that analyzed your personal and professional habits, etc.: https://www.assessmentday.com/ccat-criteria.htm
I laughed in their face and walked away. Guess that shows my personality, eh? Bullet dodged.