Where to find interesting and challenging problems in Physics and Math?

[Tazerfish]

Summary: I would like to know your favorite (freely accessible) resources and exercises.
Preferably not ordered by topic, university (bachelor) level and requiering some creative thinking/ no overly tedious calculations.

I was not sure where to put this, feel free to place this thread in another category if you are an admin.

Let me start by giving some background:
I am a fourth semester physics student and have previously participated in my country's (germany) selection process for the International Physics Olympiad (IPHO).

I really enjoyed the "puzzle" aspect of the exercises and I still "chase" problems like the one we were given in preperation for IPHO.

Recently I have come to regret that even now, after only four semesters, a lot of what I have learned is fading in my memory, and the best way to refresh this knowledge is doing problems IMO.
They provide a good indicator to what you have and have not understood /remembered.

They should ideally cover a wide range of topics, be challenging and require some tricks or outside the box thinking. (and be solvable in more than one way)

Some examples of the sort of problems I am looking for:
-IPHO exercises
-Harvards Problems of the week
-publicly accessible exams from previous semesters

The web is full of classical mechanics problems and I like solving them, but exercises for more advanced topics are harder to come by, especially for more theoretical physics.

I am looking forward to your replies.
What do you do to keep your minds fresh and dust from collecting on knowledge of previous semesters ?

 

[Wrichik Basu]

One very recommended book in Maths is Problem Solving Strategies by Arthur Engel. I am not interested in mathematics unless it has a direct application in physics, so I never read or solved problems from this book. But this is a favourite among the ones competing for the olympiads at the national level. One person had said that the book even has some problems, to which no solutions have been found to date.

The book is highly priced, however (on Amazon, it is $81). But if you have access to a library, you can borrow it and click photos of the necessary pages and work them out.

 

[archaic]

Irodov's Problems in general physics contains good physics problems I guess.