The present book is a continuation of Hungarian Problem Book III, #42 in the Anneli Lax New Mathematical Library Series. It is the translation of the second half of Volume Two of the original Hungarian work. It covers the years from 1947 to 1963, except that the competition was not held in 1956 because of political events, as was the case from 1944 to 1946. After World War II, the competition was renamed after the mathematician József Kürschák instead of after the physicist Loránd Eötvös.

The underlying philosophy of this book is the same as its predecessor. We assume that the reader is familiar with Book III, and will not duplicate the discussions conducted there. The two books should be used in conjunction.

The present book consists of four chapters. In Chapter 1, the contest problems are given in chronological order. There are forty-eight problems altogether. They are classified by subject into twelve sets. Within each set, the four problems are listed in ascending order of estimated difficulty. A Problem Index facilitates the location of solutions to individual problems.

In Chapter 2, the Theorems in Hungary Problem Book III are restated, and additional theorems are provided with proofs. In Chapter 3, the solutions to the problems are given set by set.

In Book III, we referred to Pólya's four-step method in problem-solving, focusing primarily on the first three steps, namely, understanding the problem, making a plan, and carrying out the plan. In this book, we will focus on the fourth step, looking back. This is carried out in Chapter 4.

The high school helpers I engaged when I worked on Book III have since moved on in various directions.