Team selection
This section contains detailed information about the selection for IMO, EGMO, and RMM. Contestants participate in several exams, described briefly in this table.
| Exam | Approximate Dates | Problems | Time |
|---|---|---|---|
| TSTST | Late June | 9 | 4.5h × 3 |
| December TST | Early December | 3 | 4.5h |
| January TST | Mid-January | 3 | 4.5h |
| RMM Day 1 | Late February | 3 | 4.5h |
| APMO | Mid-March | 5 | 4h |
| USAMO | March/April | 6 | 4.5 × 2 |
Selection process
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All students at MOP take the TSTST. In addition, students not at MOP may participate remotely in TSTST under any of the following circumstances:
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Any student invited to that year's MOP but who declines the invitation.
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Any student who is in the top 12 IMO selection indices of the previous year (after graduating seniors are removed), either before or after the USAMO.
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Any student who is in the top 8 EGMO selection indices of the previous year (after graduating seniors are removed), or who attended the EGMO.
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The top approximately 24 scores on TSTST (after graduating seniors are removed) form that year's IMO selection group, and qualify for December TST, January TST, RMM Day 1, APMO.
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The EGMO selection group shall follow one of two procedures depending on the results of the TSTST, up to discretion of the EGMO team leader.
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The female students who qualify for IMO selection automatically qualify for the EGMO team as long as they complete the IMO TST in December and January. The remaining female students form the EGMO selection group, and the selection process for these students will be independent of that for the IMO (the exams in December and January will be different than those given to the IMO group).
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No "automatic qualification" occurs, and all female students comprise the EGMO selection group, and they will take the same exams in December and January as the rest of the IMO selection group.
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The RMM team is determined by the index
\[\Sigma_{\text{RMM}} \coloneqq \text{TSTST} + 2 \times (\text{Dec} + \text{Jan}) \le 147.\]Based on this index, the MAA will invite four students who have not attended either RMM or IMO in the past as members of the official team to Romania. In addition, depending on the annual regulations of the RMM and budget constraints, some additional students may be invited to attend as individuals for the on-site competition. (All these papers from Day 1 will be re-graded anonymously for the purposes of TST.)
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The EGMO team is determined by the index
\[\Sigma_{\text{EGMO}} \coloneqq \text{TSTST} + 2 \times (\text{Dec} + \text{Jan}) \le 147.\]Based on this index, the MAA will invite four students to comprise the EGMO team (including automatic qualifications from item 3).
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We expect contestants in the IMO group to qualify for the USAMO through that year's AMC and AIME as usual. The AMC director may grant discretionary exceptions, but this is not guaranteed.
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The IMO team is determined by the index
\[\Sigma_{\text{IMO}} \coloneqq \text{Dec} + \text{Jan} + \text{RMM Day 1} + 0.6 \times \text{APMO} + \text{USAMO} \le 126.\]Based on this index, the MAA will invite six students to comprise the IMO team.
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If students have the same numerical index (that is, the values of \(\Sigma_{\text{RMM}}\), \(\Sigma_{\text{EGMO}}\), or \(\Sigma_{\text{IMO}}\) are equal to the same real number), a tie-breaking algorithm will be applied by dropping problems (i.e. removing problems from the weighted sum \(\Sigma_{\bullet}\)) in a specified total order until the tie is broken. The order is given as follows:
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For \(\Sigma_{\text{RMM}}\) and \(\Sigma_{\text{EGMO}}\), the order (from first to last) is TSTST 1, TSTST 4, TSTST 7, Dec TST 1, Jan TST 1, TSTST 2, TSTST 5, TSTST 8, Dec TST 2, Jan TST 2, TSTST 3, TSTST 6, TSTST 9, Dec TST 3, Jan TST 3.
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For \(\Sigma_{\text{IMO}}\), the order (from first to last) is APMO 1, APMO 2, Dec TST 1, Jan TST 1, RMM 1, APMO 3, USAMO 1, USAMO 4, Dec TST 2, Jan TST 2, RMM 2, APMO 4, USAMO 2, USAMO 5, Dec TST 3, Jan TST 3, RMM 3, APMO 5, USAMO 3, USAMO 6.
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Here is an equivalent general description of the orders. For \(\Sigma_{\text{IMO}}\), drop APMO 1 and APMO 2 first (in that order). Now all tests have three remaining problems on each day. Then one drops the first remaining problem on each day, from oldest to newest. Then do the same for the second problem on each day, then the third problem on each day.
The algorithm terminates immediately as soon as the tie is broken. Thus, it always terminates unless (and only unless) the students have identical scores on every problem used in the sum. In this unlikely case, for \(\Sigma_{\text{RMM}}\) and \(\Sigma_{\text{EGMO}}\), first compare the most recent USA(J)MO scores. (If those are equal, use the same algorithm on those 6 problems too, with the same order. If some students took USAMO and others took USAJMO, pick the USAMO students first.) Finally, use the numerically highest qualification index (\(\text{AMC} + 10 \times \text{AIME}\)), each student most recently achieved in the most recent cycle of the AMC's. If the tie is still not broken, the MAA decides arbitrarily.
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Grading and appeals
ID numbers
For this selection cycle, each USA student at MOP will be given an ID number. This is a positive integer between \(100\) and \(999\) whose prime factors are all from the set \(\{2,3,5,7\}\).2
Each paper is read anonymously by two or more TA's, as usual.
Distributions returned to students
For TSTST, papers are returned in person.
For December, January, RMM, APMO, students will receive by email the distribution of their score on each problem. We will usually also publish statistics about each individual problem.
Appeals
We permit students to appeal their scores on all exams if they believe a genuine mistake or clerical error has been made. Appeals should usually be reserved for cases where the student believes their solution is essentially correct, but the student received a low score and cannot figure out where the issue is.
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For TSTST, appeal details will be provided at the camp; there will be one designated person who receives all appeals. Students should otherwise not discuss anything about their submissions with staff.
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For the year-round exams, appeals should be submitted by email to AMCHQ within 48 hours of receiving scores.
After an appeal, the graders may adjust the score for that problem, either up or down, and that score cannot be further contested. However, based on experience from the last five years, we estimate that about 98%-99% of appeals do not result in changed score.
Starting for the 2024-2025 school year, appeals should not carry an accompanying justification. That is, a score appeal is simply a request to recheck a specific script. Any accompanying explanation submitted via an appeal to the MAA will be discarded and will not be forwarded to the graders for review.
We want to stress that appealing is not meant to be IMO-style coordination. Disagreement with the harshness of the rubric is not a valid reason to protest: the standards for TST are intentionally quite different than for IMO.