Question: In the eight queens problem, eight queens must be placed on a chessboard in such a way that no pair of queens is currently threatening





In the eight queens problem, eight queens must be placed on a chessboard in such a way that no pair of queens is currently threatening one another. One possible solution to the eight queens problem is this: In any solution to the eight queens problem, all the empty squares on the chessboard are threatened by at least two queens. We refer to a square that is threatened by exactly two queens as safe. These squares are marked here in green: For the given configuration of queens, there is only one way to put four kings on the safe squares such that no two kings are currently threatening one another: With apologies to standard chess notation, we can describe the locations of the queens and kings on this board using the following two lists of coordinates: [(0,2),(1,5),(2,3),(3,1),(4,7),(5,4),(6,6),(7,0)] [(1,7),(3,0),(7,1),(7,3)] For n=14, an nn board and the following queen configuration: [(0,1),(1,9),(2,7),(3,5),(4,3),(5,12),(6,10),(7,13),(8,11),(9,6),(10,4),(11, 2),(12,0),(13,8)] Is it possible to find arrangement of n kings. One such arrangement is [(0,0),(1,10),(2,0),(4,0),(4,2),(9,2),(9,9),(11,0),(11,7),(11,11),(13,5),(13, 9),(13,11),(13,13)]. There are 41 possible arrangements of n kings in total. Your goal: Find a placement of n=20 queens on an nn board such that no pair of queens threatens each other, and the number of different ways to place n kings on the safe squares without any pair of kings currently threatening one another is 48 . Supply your Python code and answer in a list of the queen positions, as in the above example. A bonus "*" will be given for finding a placement of n queens on an nn board such that no pair of queens is currently threatening one another, and there is no way to place n kings on the safe squares without any pair of kings threatening each other, for n26
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