Question 1
Alice writes an arithmetic progression of $n>2$ distinct numbers. Bob writes their reciprocals in some order and also obtains an arithmetic progression. Which values of $n$ are possible? The reciprocals require all original numbers to be nonzero, as stated explicitly in the official original. (5 points)
Neutral editorial illustration.
Practice scoring adds all whole-question scores (maximum 56). Official ITOT scoring adds only the three highest whole-question scores (maximum 30), after summing subparts within each question. The importer does not enforce best-three scoring. Duration: 300 minutes from historical organizer general rules, not an individually printed duration on this paper.
Neutral editorial illustration.
Practice scoring adds all whole-question scores (maximum 56). Official ITOT scoring adds only the three highest whole-question scores (maximum 30), after summing subparts within each question. The importer does not enforce best-three scoring. Duration: 300 minutes from historical organizer general rules, not an individually printed duration on this paper.