Knight's Tour is NP-hard on connected boards; optimal Knight Exchange is NP-hard by polynomial-time reduction from the tour problem.
Schwenk (1991).Which Rectangular Chessboards Have a Knight’s Tour? Mathematics Magazine, 64, 325–332
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The Optimal Knight Exchange Puzzle is NP-Hard
Knight's Tour is NP-hard on connected boards; optimal Knight Exchange is NP-hard by polynomial-time reduction from the tour problem.