n-Queens problem: For a Knight to capture all Queens there…
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n-Queens problem: For a Knight to capture all Queens there is only one solution for n>10
The n-Queens problem involves placing n Queens on a chess board of size nxn, without having any of the queens attacking each other. I have expanded this problem to include a single knight, with the question: Is the knight able to capture all queens on the board? The rules are as follows:
The Queens must be placed so they are not attacking each other. Queens do not move
The Knight starts on a single Queen space, and that Queen is removed
The knight cannot be on a square attacked by any queen, but removing a queen frees up 'safe' spaces. The knight can traverse and revisit safe spaces
The first Queen a Knight takes (apart from initial placement) must be within knight-attack range, because there are no other safe spaces available at the start
Solutions have been found for n= 4,5,7,8,9,10,17
and proved impossible for 6,11,12,13,14,15,16,18,19
The real curiosity is n=17 where a single solution has been found from over 95 million possibilities. Anything above 19 is open and has not been tested.
Link to paper (pdf): https://drive.google.com/file/d/1zfugBiIZi4xrhDjM-x1YtDlf3M-SFlXv/view?usp=sharing
UPDATE: n20 has no solutions, leaving n17 as the largest solution
UPDATE: n21 has no solution
#science
The n-Queens problem involves placing n Queens on a chess board of size nxn, without having any of the queens attacking each other. I have expanded this problem to include a single knight, with the question: Is the knight able to capture all queens on the board? The rules are as follows:
The Queens must be placed so they are not attacking each other. Queens do not move
The Knight starts on a single Queen space, and that Queen is removed
The knight cannot be on a square attacked by any queen, but removing a queen frees up 'safe' spaces. The knight can traverse and revisit safe spaces
The first Queen a Knight takes (apart from initial placement) must be within knight-attack range, because there are no other safe spaces available at the start
Solutions have been found for n= 4,5,7,8,9,10,17
and proved impossible for 6,11,12,13,14,15,16,18,19
The real curiosity is n=17 where a single solution has been found from over 95 million possibilities. Anything above 19 is open and has not been tested.
Link to paper (pdf): https://drive.google.com/file/d/1zfugBiIZi4xrhDjM-x1YtDlf3M-SFlXv/view?usp=sharing
UPDATE: n20 has no solutions, leaving n17 as the largest solution
UPDATE: n21 has no solution
#science
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