BALKAN-SL 2014 C1
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)?
Dataset text AI-MO AoPS. Quoted with source.
Solutions
No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.