Queen's Domain
A queen stands on an otherwise empty standard ( ) chessboard.
What is the maximum number of squares that are accessible to the queen in a single valid move?
Assumption :
Standing still does not count as a move.
The answer is 27.
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1 solution
Relevant wiki: Chess Puzzles
The number of "rook-like " moves that the queen can make , starting from any square, is always 1 4 , so it suffices to maximise the number of "bishop-like" moves. Note that the "rook-like" and "bishop-like" moves are mutually exclusive and exhaustive.
Note that a diagonal in a chessboard can have at most 8 squares, and at most 7 other squares that a queen can access if she is already on that diagonal. So there can be at most 7 + 7 = 1 4 "bishop-like" moves she can make. But equality can't hold, because the two longest diagonals are oppositely coloured. So no more than 1 3 such moves can be made. Equality can clearly hold when the queen stands on some central square.
The answer is 1 4 + 1 3 = 2 7 .