Combinatorics · Extremal combinatorics · Grid coloring · Parity
A table of dimensions \(2010 \times 2011\) is given. Determine the largest number of cells that can be colored so that every \(2 \times 2\) square of the table contains at most two colored cells.
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Serbian Municipal Competition 2011, high school grade I, category A, problem 3. Organized by the Mathematical Society of Serbia (DMS). Source