Short answers, pulled from the story.
The American Invitational Mathematics Examination began in 1983 as a single annual event scheduled for late March or early April on either a Tuesday or Thursday. For seventeen years, the test appeared only once per year to select high school students from the top five percent of AMC 12 participants.
Starting in 2010, the criteria expanded to include the top 2.5 percent of AMC 10 scorers as well as those ranking in the top five percent on the AMC 12 high school mathematics examination. By 2022, the organization adjusted these percentages to invite approximately the top 13 to 15 percent of AMC 12 participants and roughly the top 6 to 8 percent of AMC 10 participants.
Each answer must be an integer between 000 and 999 inclusive with leading zeros filled in so that 7 becomes 007 and 43 becomes 043. Participants cannot use calculators but are permitted pencils erasers rulers and compasses while answers are entered onto an OMR sheet similar to grid-in math questions on the SAT.
Starting with the current cycle, the system now adds the AMC score to twenty times the AIME score to produce a single index used to set qualification cutoffs. Since 2017, the USAMO and USAJMO qualification cutoff has been split between the AMC A and B contests as well as the AIME I and II versions resulting in eight published USAMO and USAJMO qualification cutoffs per year.
The rapid spread of the COVID-19 pandemic led to the cancellation of the AIME II for that year. Instead qualifying students were able to take the American Online Invitational Mathematics Examination which contained problems originally intended for the second date.