Question 1
SEAMO self-study edition 2027; not an official 2027 paper. Original source years are retained. 25 questions, 90 minutes; Q1–10: 3 points, Q11–20: 4 points, Q21–25: 6 points, total 100. Original response types and all subparts are preserved. Verified is an editorial convention; source defects, necessary assumptions and unresolved mathematical uncertainty are disclosed.
A network of domestic flights is set up in the country of Utopia. A city is directly connected to at most 3 others, and there is at most 1 transit flight from one city to another. What is the maximum number of cities in Utopia?
Interpret the routes as two-way connections, and “at most 1 transit” as at most one intermediate city: any city must be reachable from any other in at most two flights.
A network of domestic flights is set up in the country of Utopia. A city is directly connected to at most 3 others, and there is at most 1 transit flight from one city to another. What is the maximum number of cities in Utopia?
Interpret the routes as two-way connections, and “at most 1 transit” as at most one intermediate city: any city must be reachable from any other in at most two flights.