What is Reddit's opinion of Combinatorial Problems and Exercises (AMS Chelsea Publishing)?

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Get your combinatorics on with Combinatorial Problems and Exercises by Laszlo Lovasz.

Great text that ramps up pretty quick into what I consider post-grad material, but I love how it's arranged: Problems, Hints on the Problems, Answers to the Problems.

I didn't get very far (yet! Someday...) but it could be used as a good guide to looking into combinatorics problems, which I think are cool and underrated and sadly often relegated to some side-note in a discrete class.

Here are some very good books that are thorough and encyclopedic, with a very example-based or problem-based approach. So not necessarily the very best books to teach you a topic, but incredibly useful and valuable as reference works.

Analysis:
Problems and Theorems in Analysis, by Polya and Szego

Probability:
Univariate Discrete Distributions, by Johnson, Kemp, and Kotz

Combinatorics:
Combinatorial Problems and Exercises, by Lovasz
Handbook of Combinatorics, by Graham, Grotschel, and Lovasz

Personally, I enjoy https://projecteuler.net/archives (but understand, that for some problems, you would assume that the computation power you'd need is really large, however, there's almost always a more elegant solution.)

If you get bored with that, I'd really recommend https://www.amazon.com/Combinatorial-Problems-Exercises-Chelsea-Publishing/dp/0821842625. The book is absolutely incredible and there's a rumor (unconfirmed) that if you're a grad student in Hungary and you're unable to solve all the problems in this book, you should quit grad school. (I'm aware this is a joke, but given the number of brilliant mathematicians who were from Hungary, I'm not so sure anymore)