What is the least number of knights needed to cover the entire board?
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?
theory knights
edited Dec 19 at 10:52
fkraiem
1053
asked Dec 16 at 23:20
Rewan Demontay
12519
add a comment |
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?
theory knights
edited Dec 19 at 10:52
fkraiem
1053
asked Dec 16 at 23:20
Rewan Demontay
12519
16
What do the green squares represent?
– Pikamander2
Dec 17 at 5:52
add a comment |
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?
theory knights
edited Dec 19 at 10:52
fkraiem
1053
asked Dec 16 at 23:20
Rewan Demontay
12519
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?
theory knights
theory knights
edited Dec 19 at 10:52
fkraiem
1053
asked Dec 16 at 23:20
Rewan Demontay
12519
edited Dec 19 at 10:52
fkraiem
1053
asked Dec 16 at 23:20
Rewan Demontay
12519
edited Dec 19 at 10:52
fkraiem
1053
edited Dec 19 at 10:52
fkraiem
1053
edited Dec 19 at 10:52
fkraiem
1053
1053
asked Dec 16 at 23:20
Rewan Demontay
12519
asked Dec 16 at 23:20
Rewan Demontay
12519
asked Dec 16 at 23:20
Rewan Demontay
12519
12519
16
What do the green squares represent?
– Pikamander2
Dec 17 at 5:52
add a comment |
16
What do the green squares represent?
– Pikamander2
Dec 17 at 5:52
16
16
What do the green squares represent?
– Pikamander2
Dec 17 at 5:52
What do the green squares represent?
– Pikamander2
Dec 17 at 5:52
add a comment |
1 Answer
1
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oldest
votes
Depending on whether occupied squares need to be covered as well, the number is:
- 12 knights (without covering occupied squares)
- 14 knights (with covering occupied squares)
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 at 0:02
user1583209
12k21553
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 at 19:45
I tried to include a diagram, but did not succeed. Is it possible to show impossible (no Kings) positions?
– user1583209
Dec 17 at 20:47
add a comment |
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1 Answer
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active
oldest
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1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
Depending on whether occupied squares need to be covered as well, the number is:
- 12 knights (without covering occupied squares)
- 14 knights (with covering occupied squares)
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 at 0:02
user1583209
12k21553
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 at 19:45
I tried to include a diagram, but did not succeed. Is it possible to show impossible (no Kings) positions?
– user1583209
Dec 17 at 20:47
add a comment |
Depending on whether occupied squares need to be covered as well, the number is:
- 12 knights (without covering occupied squares)
- 14 knights (with covering occupied squares)
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 at 0:02
user1583209
12k21553
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 at 19:45
I tried to include a diagram, but did not succeed. Is it possible to show impossible (no Kings) positions?
– user1583209
Dec 17 at 20:47
add a comment |
Depending on whether occupied squares need to be covered as well, the number is:
- 12 knights (without covering occupied squares)
- 14 knights (with covering occupied squares)
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 at 0:02
user1583209
12k21553
Depending on whether occupied squares need to be covered as well, the number is:
- 12 knights (without covering occupied squares)
- 14 knights (with covering occupied squares)
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 at 0:02
user1583209
12k21553
edited Dec 17 at 0:11
answered Dec 17 at 0:02
user1583209
12k21553
answered Dec 17 at 0:02
user1583209
12k21553
answered Dec 17 at 0:02
user1583209
12k21553
12k21553
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 at 19:45
I tried to include a diagram, but did not succeed. Is it possible to show impossible (no Kings) positions?
– user1583209
Dec 17 at 20:47
add a comment |
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 at 19:45
I tried to include a diagram, but did not succeed. Is it possible to show impossible (no Kings) positions?
– user1583209
Dec 17 at 20:47
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 at 19:45
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 at 19:45
I tried to include a diagram, but did not succeed. Is it possible to show impossible (no Kings) positions?
– user1583209
Dec 17 at 20:47
I tried to include a diagram, but did not succeed. Is it possible to show impossible (no Kings) positions?
– user1583209
Dec 17 at 20:47
add a comment |
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16
What do the green squares represent?
– Pikamander2
Dec 17 at 5:52