As far as book are concerned, my favorite basic combinatorics books are Basic Techniques of Combinatorial Theory by Daniel I.A. Cohen and Combinatorics and Graph Theory by Harris, Hirst and Mossinghof. Cohen, in particular, is a great resource for questions which will make you think deeply and expand your horizons. Most chapters have well over 70 exercises, ranging from rountine to quite difficult. Since the quality of questions seems paramount to your decision I will include an example exercise from Cohen:
A collection of $n$ lines in the plane are are said to be in general position if no two are parallel and no three are concurrent. Let $a_n$ be the number of regions into which $n$ lines in general position divide the plane. How big is $a_n$?
And this is just the tip of the iceberg. Cohen's book is full of high-quality exercises, most of which have attributions to the originators.
Something that really sets Cohen's treatment of the topic apart from others is the fact that he often gives 2 or 3 different proofs of theorems. Unfortunately, the book is out of print; however, there are still many used copies for sale on Amazon.
Combinatorics and Graph Theory by Harris, Hirst and Mossinghof covers much of the same basic combinatorial material as Cohen. To me, what really sets this book apart is the inclusion of infinitary combinatorics, particularly their treatment of Ramsey theory.
If you are looking for a more advance treatment of combinatorics, then you will find Enumerative Combinatorics by Richard Stanley more than accommodating, with hundreds of difficult exercises, some of which (at least at the time of writing) are unsolved.