Looking for set of combinatorics problems

Question

I'm preparing to Mathematics for Computer Science exam. What I learned from past edition of exams is fact of very often occurence of old problems. I mean more or less known problems, but possible to find in some sources. For example "expected number of cycles in permutation", "problem of 100 prisoners" or according to combinatorical proof: "problem of counting specific variations of lattice paths" or "coutnig number of functions with requirements".

Please be so kind to suggest me some websites/textbooks/topics on stack with set of exercises of such a type.

Greetings M.

Answer 1

MIT has free lecture notes on combinatorics which are pretty concise and well written. I found it to be a good introduction (and I didn't need to attend the lectures to benefit from it).

Answer 2

I believe the type of combinatorics probems you are looking for is non-enumerative i.e. you don't need to count the number of objects satisfying a given property, rather you have to understand algorithms, processes, recursions etc.. Note that it will still help to have a good knowledge of enumeratve combinatorics. You should check out Problem Solving Strategies by Arthur Engel. It lists huge number of problems on PHP, invariance and monovariance, induction, enumerative combinatorics etc..

You should also check out this book. It's one of the best that I have seen for olympiad combinatorics which aren't of enumerative type.