1995 OIM Problems/Problem 4

Problem

Pieces are placed on a board with $m \times n$ squares. Each piece placed on the board "dominates" all the squares in the row (-), column (|) and diagonal (\) to which it belongs (*). Find the smallest number of pieces that must be placed so that all the squares on the board are "dominated."

Note (*): Note that the piece does not "dominate" the diagonal (/).

~translated into English by Tomas Diaz. ~orders@tomasdiaz.com

Solution

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See also

https://www.oma.org.ar/enunciados/ibe10.htm