Fazekas, one of the most famous secondary school in Budapest has built up its considerable reputation by providing a stimulating environment for talented young people. The school is simply called prodigy-factory among teachers and students, where excellent teachers mind versatile minds.
Once upon a time in this spirit two young and enthusiastic maths teachers (Tünde Fazekas and András Hraskó) has established a habit of setting up series of maths exercises each week for their 13-14 year old pupils mainly about problems which haven’t been published yet. The solutions were thoroughly analyzed, in fact refining and preparing the arguments ready for publication proved to be the major part of their job. This way a unique book has been produced in both, mathematical and didactic sense.
Two world-famous Hungarian mathematicians, Miklós Laczkovich and László Lovász recommends the volumes: Thinking about mathematical problems is like going for an exploration of uncharted territories. One doesn’t know which path to choose; on the way unknown dangers are lurking around the explorers; one might fall into a trap or can get lost in the jungle; if one had successfully negotiated a difficult path and reached a sunny clearance a difficult decision has to be taken: should one carry on in the same direction or it’s better to turn back and follow a new path? When the explorers reach their destination they immediately should ask themselves: might there be easier or quicker ways of getting here? Perhaps going in an unexpected direction taking only one or two steps? After having reached the destination a new territory reveals itself: it would be worth exploring that as well! The Maths Exercises for Eager Young Hobbits guides the reader into these adventures. One learns that the destination can be approached from many different directions: four or even more different solutions are shown for each exercise, including ingenious ones using only one or two steps. The possible general conclusions drawn keep instigate new explorations. The authors usually show the reader the faulty solutions as well, so that s/he could learn from traps and dead ends, and next time could avoid them. I heartily recommend these volumes for everybody who wants to experience the spiritual adventures of solving mathematical problems.
Miklós Laczkovich I’m happy to recommend these volumes of maths exercises compiled by the teachers and pupils of Fazekas Gimnázium.
I was very lucky to be once a pupil of this high school as one of the members of the then newly organized class specialized in maths. We had excellent teachers: our maths teacher, Imre Rábai provided us with not only thorough and enthusiastic classes but he invited quite a few representatives of the Hungarian research mathematicians, including two would be Academics (András Hajnal and Pál Révész). But beside this, to be in a constant friendly competition with my classmates was also equally important. „I have a problem for you, you have 4 minutes to solve it!” - was a common way of addressing each other.
Solving problems is only one part of the mathematical thinking (the other parts include creating notions, setting up theories, planning algorithms and so on), but the problem-solving skills acquired in Fazekas have proved to be fundamentally important in my practical mathematical works. Especially during solving problems in maths competitions one can acquire an ability of distinguishing promising and not so promising ideas, or that of recognizing dead ends on time and avoiding them.
These volumes testify that the famous spirit of Fazekas is still very much alive and kicking, and the teachers and pupils cultivate maths with as much enthusiasm and loving care as they did when I went there. I wish the Reader many entertaining and informative hours of problem-solving!

László Lovász