This one I have been searching for a while. I had read reference to this work in some book (which I don’t remember now),  and ever since was trying to find it. Luckily today I landed on a page (Edit: 8 Nov 23, added wayback machine link) which had link to this book, thanks to Alex for putting up this book.

This is the direct link to the pdf.

The ‘book’ seems to be is a part of a larger book, maybe selected/complete works Collected Papers of of P. L. Kapitza last chapter (32) of last volume (4). Also see comment of Alex). I do not know the original source. It has but 19 pages and there are 224 problems, and no solutions. But don’t be fooled by the number of pages. These are some of the most interesting and difficult problems you will encounter, and you will perhaps need all your wits to get through them. But they are fun, and you will enjoy doing them, even if some are very difficult. So don’t be disheartened if, you cannot solve them at all. But they will certainly set you thinking for sure.

This is what Kapitza writes about them:

The problems published in this collection were compiled by me for students of the Moscow Physical-Technical Institute, where I taught a course in general physics in 1947-1949. The collection also includes problems given at examinations for postgraduate studies at the Institute of Physical Problems at the USSR Academy of Sciences.

And on the characteristics of the problems:

I strove to achieve this end by formulating the majority of questions in the following manner. A small problem is presented, and the student, using the known laws of physics, must analyse and describe quantitatively the natural phenomenon involved. These natural phenomena were selected in terms of their scientific or practical interest within the scope of the students’ level of knowledge.

A characteristic feature of our problems is that they have no definite answer because the student is allowed to proceed further and further with the analysis of the problem posed, depending on his own abilities and inclinations.

Most of the problems have another distinctive trait. They do not contain numerical values of physical constants or parameters, and the student has to choose them personally.

And on how they were conducted

In the examinations, the students were always given complete freedom to use literature for solving the problems. Usually a few (up to 5) problems were given per examination, so as to enable the students to choose 23 of them. Thus, the inclinations of a student could be gauged from his selection of problems. For postgraduate examinations, new and more complex problems were prepared; in these cases, however, the student was allowed not only use of literature but also freedom to seek advice. Indeed, the scientist must cultivate the skill of using the advice of others, apart from learning the use of literature. In scientific work, discussions and consultations with colleagues and instructors are essential for success; this) however, requires a proper training from the very beginning of the studies.

We usually allowed about one hour for the solution of each problem. All problems have to be solved in writing, but the capabilities and character of the student become evident mostly 1n the course of a verbal discussion of the written text.