> 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 sometimes remind myself that (i) I don't have to re-derive all mathematics from scratch and that (ii) there are always more problems to do.

>4) You've got to get to the end of the book. Matter of pride.

This is your secret.

What was your strategy when a textbook didn't have answers to all of the exercises?

Even if you are self-studying, you can and should occasionally go talk to someone who knows the subject well to help you with the question. If you don't know anyone, post the question online.

personally I bought solved problems in a step by step form in a separate book to supplement.

This works for me as well. I'd add another point:

* Acknowledge that sometimes the book you're reading is repetitive or not very well written. If you're <10% in, read up on reviews and try to find a better book on the same subject. If ≥10%, commit and complete, acknowledging that you're not necessarily the best judge of a book's quality.

I guess discipline and consistency.