Combinatorics · Board placement · Extremal combinatorics · Construction and bound · Pigeonhole
What is the largest number of chips that can be placed on the cells of a \(7 \times 7\) board so that no rectangle of area \(6\), with sides running along the grid lines, contains more than one chip?
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Serbian Municipal Competition 2013, high school grade I, category A, problem 5. Organized by the Mathematical Society of Serbia (DMS). Source