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The USAMO (and the USAJMO since 2010) is restricted to approximately 500 (250 prior to 2006) participants combined each year. To keep this quota constant, the AMC Committee uses a selection process, which has seen a number of revisions in the competition's history.
Until 2011, only black group MOPpers were eligible for the selection to the USA IMO team, determined by combining USAMO results with results of a similar competition called the Team Selection Test (TST). From 2011, a new competition called the Team Selection Test Selection Test (TSTST) was established.
The student only needs to reach one qualification cutoff to take the USAMO or USAJMO. During the 1990s, it was not uncommon for fewer than 2,000 students to qualify for the AIME, although 1994 was a notable exception where 99 students achieved perfect scores on the AHSME and the list of high scorers, which usually was distributed in small ...
AIME introduced in 1983, now is a middle step between AHSME and USAMO. AJHSME, now AMC 8, introduced in 1985 2000–present American Mathematics Competition 25 -5 Questions AHSME split into AMC10 and AMC12 A&B versions introduced in 2002. USAMO split into USAJMO and USAMO in 2010.
In 1995, four freshmen-and-under took the USAMO. I believe that as late as 1998 (and as early as 1991) it was still the case that they drew a cutoff for seniors and a lower cutoff for underclassmen -- and that was the entire process. Also the first few USAMOs just invited the top 100 guys on the AHSME, as the USAMO pre-dates the AIME.
Championnat International de Jeux Mathématiques et Logiques — for all ages, mainly for French-speaking countries, but participation is not limited by language.; China Girls Mathematical Olympiad (CGMO) — held annually for teams of girls representing different regions within China and a few other countries.
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Ciprian Manolescu (Romania) managed to write a perfect paper (42 points) for gold medal more times than anybody else in the history of the competition, doing it all three times he participated in the IMO (1995, 1996, 1997). [91] Manolescu is also a three-time Putnam Fellow (1997, 1998, 2000). [92]