no 4 brings bad luck, max no to be seated in a row of capacity 55 seats
Source: Balkan BMO Shortlist 2014 C1
August 6, 2019
combinatorics
Problem Statement
The International Mathematical Olympiad is being organized in Japan, where a folklore belief is that the number brings bad luck. The opening ceremony takes place at the Grand Theatre where each row has the capacity of seats. What is the maximum number of contestants that can be seated in a single row with the restriction that no two of them are seats apart (so that bad luck during the competition is avoided)?