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Found problems: 2

Russian TST 2017, P1
Tags: combinatorics , board , chess king
What is the largest number of cells that can be marked on a $100 \times 100$ 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.)

KoMaL A Problems 2023/2024, A. 881
Tags: chessboard , chess king , combinatorics
We visit all squares exactly once on a $n\times n$ chessboard (colored in the usual way) with a king. Find the smallest number of times we had to switch colors during our walk. [i]Proposed by Dömötör Pálvölgyi, Budapest[/i]