Shade 32 cells, four on each row and column, of an 8 x 8 blank chessboard (all its cells originally white) so that a rook sitting on any shaded cell can reach any other shaded cell, moving just along other shaded cells.
If not possible, what is the size of the largest square board on which this can be done, i.e. shading four cells of each row and column creating a connected territory for a rook lying on any of its cells.
Problem based on a similar one communicated by Stan Wagon (http://stanwagon.com/pow/), who asks whether 3 cells of each row and column can be so shaded in a n x n (n > 4) board.