A beautiful book from Eastern Europe for Math Olympiads, ISI CMI Entrance and joy of doing math

Selected Problems and Theorems in Elementary Mathematics – Arithmetic and Algebra by D. O. Shklyarsky,  N. N. Chentsov and I. M. Yaglom. T

This book contains The conditions of problems, the answers and hints  to them and the solutions of the problems. The conditions of the most difficult problems are marked by stars. We recommend the reader to start with trying to solve without assistance the problem he is interested in. In case this attempt
fails he can read the hint or the answer to the problem, which may facilitate the solution, Finally, if this does not help, the solution of the problem given in the book should be studied. However, for the starred problems it may turn out to be appropriate to begin with reading the hints or the answers before proceeding to solve the problems.