Playing chess on an infinite chessboard

Brilli has an infinite chessboard, in which an 8 × 8 8×8 subboard is marked as Sacred. In order to preserve the Sanctity of this chessboard, her friend Brian wishes to place some indistinguishable Holy Knights on the chessboard (not necessarily within the Sacred subboard) such that:

  • No two Holy Knights occupy the same square;

  • Each Holy Knight attacks at least one Sacred square;

  • Each Sacred square is attacked by exactly one Holy Knight.

In how many ways can Brian protect the Sanctity of Brilli’s chessboard? (A Holy Knight works in the same way as a knight piece in chess, that is, it attacks any square that is two squares away in one direction and one square away in a perpendicular direction. Note that a Holy Knight does not attack the square it is on.)


The answer is 7056.

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