5th All Soviet Union Mathematical Olympiad 1971 Problems & Solutions

1.  Prove that we can find a number divisible by 2n whose decimal representation uses only the digits 1 and 2. 2.  (1) A1A2A3 is a triangle. Points B1, B2, B3 are chosen on A1A2, A2A3, A3A1 respectively and points D1, D2 D3 on A3A1, A1A2, A2A3 respectively, so that if parallelograms AiBiCiDi are formed, then the lines AiCi