Day 2 All-Russian Math Olympiad 2013 | Discrete Mathematics | Math Olympiad Training
This problem comes from the 2013 All-Russian Olympiad.
101 distinct numbers are chosen among the integers between 0 and 1000. Prove that, among the absolute values of their pairwise differences, there are ten different numbers not exceeding 100.
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The All-Russian MO is the main competition and consists of five rounds, the final (5th) round being held in late April. However, olympiads in Moscow and Saint Peterburg are held independently, and the most successful students from each of these two olympiads qualify directly for the final round of the All-Russian MO.
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