CIIM 2024 Problem 5

Day 2

Un tablero $3 \times N$ tiene inicialmente todas sus casillas pintadas de blanco. Sea $a(N)$ el número máximo de casillas que se pueden pintar de negro de manera que no haya tres casillas consecutivas (de forma horizontal, vertical o diagonal) pintadas de color negro. Demostrar que $\lim_{N \to \infty} \frac{a(N)}{N}$ existe y determinar su valor.

Official text Iberoamerican Interuniversity Mathematics Competition 2024 official paper, page 1. Quoted with source.

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