The tasks proposed at the republican mathematical olympiads of the Moldavian SSR in 1957-1985, as well as their solutions or instructions for them, are given in chronological order. Most of the 530 tasks do not require cumbersome calculations, although non-standard thinking is needed to solve them. The brevity of the above solutions will allow the reader to show his imagination. The book will interest a wide range of mathematics lovers. It can serve as a manual for mathematical circles, participants in olympiads and applicants.