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ex- USSR / Russian math competitions

Adygea Teachers' Geometry Olympiad
All Siberian Open School Olympiad
All Soviet Union Mathematical Olympiad (ASU) 1961-1992
[continued as All-Russian]
Almaty City MO (Kazakhstan)
Belarus MO
Belarus TST
Caucasus MO
Champions Tournament (Турнір чемпіонів) Ukraine
Estonia Open MO
Estonia National MO
Estonia  TST
Euler Olympiad (Juniors)
Euler Teachers' MO
European Math Tournament
Formula of Unity / Third Millenium
High Standards Olympiad (Высшая проба) Russia
Kazakhstan MO

Russian Competitions

(according to official levels of difficulty in Math) [1 is the hardest]

level 1  (order by name)
  1. All - Russian Mathematical Olympiad                                (before 1982 as All Soviet Union)
  2. High Standards Olympiad                      (Высшая проба)
  3. Moscow Mathematical Olympiad                         (MMO) (older name: Leningrad MO)
  4. Saint Petersburg Mathematical Olympiad
  5. Tournament of Towns International Mathematics   (ToT)    (before 2001)
level 2  (order by name)
  1. All-Siberian Open School Olympiad
  2. Formula of Unity / Third Millenium     
  3. Lomonosov Tournament                                                       

It is worth noting that not all student olympiads are the same. 
I level The holder of the diploma can be enrolled in a university without entrance exams.
II level The owner can get the opportunity to enter a specialized field without exams or get +100 points to the exam result.
III level gets +100 points to the exam result.
Important! Each university independently decides what benefits the winners and prize-winners of school olympiads will receive. [source]

collected pdf files
translated by S/W engineer Vladimir Pertsel

translated by D. Leites (ed.), without figures 
written by G. Galperin, A. Tolpygo, P. Grozman, A. Shapovalov, V. Prasolov, A. Fomenko

top russian olympiad links:

The Ukranian Math Magazine
U sviti matematyky  /   In the World of Mathematics
has it's own tab here

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