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FINALS - Portuguese Mathematical Olympiad (High-School) P3

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April 6, 2014
combinatorics unsolvedcombinatorics

Problem Statement

Amélia and Beatriz play battleship on a 2n×2n2n\times2n board, using very peculiar rules. Amélia begins by choosing nn lines and nn columns of the board, placing her n2n^2 submarines on the cells that lie on their intersections. Next, Beatriz chooses a set of cells that will explode. Which is the least number of cells that Beatriz has to choose in order to assure that at least a submarine will explode?
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