Fourth Week, January 31. A Chess Board Problem.Consider a chess board of 2n by 2n black and white squares. We say that two distinct squares are adjacent if they have an edge in common. A square is not adjacent to itself, nor to a square with which it only has a corner in common. What is the minimum number of pawns you must put on the chess board such that each square is adjacent to a pawn? (from the 1999 International Math Olympiad in Bucharest, Romania.)
Note: I am not giving out solutions to "Problems of the Week". But I am very happy to discuss these problems with you, including any partial or attempted solutions that you might have. I am always interested in hearing about interesting or creative solutions, so let me know if you have any!
See previous Problems of the Week.
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