> If you're having trouble with some exercise, you can look up the answer key for that specific exercise, but only after you've spent 5 minutes of effort on that specific exercise without making progress.
I've wondered what the ideal time of effort is on several occasions. Sometimes I'll get stuck on an algorithm problem and no matter what technique I try I can't make progress. Sometimes I'll try for days, until I eventually just give up. That's obviously not ideal, but I think 5 minutes is too short for this situation. I worry that I won't internalize the solution or technique very well unless I've wrestled around in the problem space for a while first.
This is a good point, and is one of the biggest pain points in self-study vs being taught by in school/expert, or having access to the collective intelligence of fellow students.
The best way to combat this is to be smart about using whatever resources available to get an expert to help you. Post questions on sites like mathoverflow/stackoverflow, and be persistent. You could waste time spending weeks on a single problem that someone with experience can solve in seconds.
Personally, this is why I don't like self-study on it's own. If you can form a study group, do a part-time degree or find some other method to ensure that you don't go down costly rabbit-holes, you should. The gains in efficiency will be worth it.
Well, getting an expert to help isn't much different than looking up the answer. My particular struggle isn't about not knowing where to find the answer, it's about when to give up trying to figure it out on my own.
I've wondered what the ideal time of effort is on several occasions. Sometimes I'll get stuck on an algorithm problem and no matter what technique I try I can't make progress. Sometimes I'll try for days, until I eventually just give up. That's obviously not ideal, but I think 5 minutes is too short for this situation. I worry that I won't internalize the solution or technique very well unless I've wrestled around in the problem space for a while first.