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Turkey EGMO TST 2017 P5

Source: Turkey EGMO TST 2017 P5

June 1, 2017
TurkeyEGMOTSTcombinatoricscontest problem

Problem Statement

In a 12×1212\times 12 square table some stones are placed in the cells with at most one stone per cell. If the number of stones on each line, column, and diagonal is even, what is the maximum number of the stones?
Note. Each diagonal is parallel to one of two main diagonals of the table and consists of 1,2,111,2\ldots,11 or 1212 cells.