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King attacks marked cells

Source: Russian TST 2017, Day 5 P1 (Group NG)

April 1, 2023
boardcombinatoricschess king

Problem Statement

What is the largest number of cells that can be marked on a 100×100100 \times 100 board in such a way that a chess king from any cell attacks no more than two marked ones? (The cell on which a king stands is also considered to be attacked by this king.)