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TOT 048 1983 Autumn J5 N^2 pieces on NxN chessboard

Source:

August 18, 2019
combinatoricsChessboard

Problem Statement

N2N^2 pieces are placed on an N×NN \times N chessboard. Is it possible to rearrange them in such a way that any two pieces which can capture each other (when considered to be knights) after the rearrangement are on adjacent squares (i.e. squares having at least one common boundary point)? Consider two cases: (a) N=3N = 3. (b) N=8N = 8
(S Stefanov)
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