I’ve seen the solutions to the lowest amount of queens, bishops, and rooks are needed to cover an entire board, as in they can attack all squares and are the only type of piece on the board. What is the solution for this with knights?
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asked Dec 16 '18 at 23:20
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18What do the green squares represent? – Pikamander2 Dec 17 '18 at 5:52
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Depending on whether occupied squares need to be covered as well, the number is:
[Title " 12 knights, Without Covering Occupied Squares"]
[FEN "8/5N2/1NN1NN2/2N5/5N2/2NN1NN1/2N5/8 w - - 0 1"]
[Title " 14 knights, With Covering Occupied Squares"]
[FEN "8/2N1NN2/2N1N3/2N3N1/2N1N3/1NN1NNN1/8/8 w - - 0 1"]
Problems like this are called domination problems and solutions for knights and other pieces as well as a reference are given on the wikipedia page on mathematical chess problems
answered Dec 17 '18 at 0:02
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You could consider increasing value of this answer by showing a layout with the resolved 14 knights [I see it as: 4 N on the 2nd rank, from C-F, 6 N on the 6th rank, from B-G, and 4 N on the 4th rank, B4, C4, F4, G4]. – Grade 'Eh' Bacon Dec 17 '18 at 19:45
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I tried to include a diagram, but did not succeed. Is it possible to show impossible (no Kings) positions? – user1583209 Dec 17 '18 at 20:47
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