Combinatorics · Pigeonhole · Double counting · Board configurations · Constructions
Ana and Branko placed a number of tokens on the squares of an \(8 \times 8\) board, no square carrying more than one token. Ana then wrote down the number of tokens in each of the eight rows, and Branko wrote down the number of tokens in each of the eight columns. All eight numbers written by Ana turned out to be different from one another. Is it possible that none of Branko's numbers appears among Ana's?
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Serbian Regional Competition 2005, high school grade I, category A, problem 5. Organized by the Mathematical Society of Serbia (DMS). Source