I have extensive recruitment experience and I understand the idea of "let's filter out as much as we can to gain time".
My experience is: it doesn't work, you will have to crawl through resumes, do phone interview and have people come over. You can be clever about what you ask in a resume and how you do your interviews but you will somehow need a list of skills and experience and somehow you will have to talk to the people you want to hire.
Additionally, you don't want people who just "find solutions to problems", you probably want people who build systems. That's a different skill set, which is why you will not filter out the right type with a teaser.
You will also unreliably assess their skills because you cannot tell how much time it took or if they actually did it.
Have people come over. Evaluate their technical and human skill. Nothing fancy, just straightforward stuff.
If in one day of interview you think they're people you'd like to work with, hire them. If you have any doubt, don't.
Let go the idea of the exam. You're a company not an university.