Discrete Peaceful Encampments: 9 queens on a chessboard
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Here's a discrete variation of yesterday's puzzle Peaceful Encampments.
You have 8 white queens and 8 black queens. Place all these pieces onto a normal 8x8 chessboard in such a way that no white queen threatens a black queen (nor vice versa).
Or, phrasing the puzzle in a way parallel to Black and white queens on an 8x8 chessboard — changing only one word from that puzzle — I would say:
What is the largest number of queens that can be placed on a regular 8×8 chessboard, if the following rules are met:
- A queen can be either black or white, and there can be unequal numbers of each type [but if so, we count the smaller population].
- A queen must not be threatened by other queens of a different color.
- Queens threaten all squares in the same row, column, or diagonal (as in chess). Also, threats are blocked by other queens [not that this matters].
Can you find a way to place more than 8 queens of each color "peacefully" on an 8x8 chessboard?
geometry chess checkerboard
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add a comment |
$begingroup$
Here's a discrete variation of yesterday's puzzle Peaceful Encampments.
You have 8 white queens and 8 black queens. Place all these pieces onto a normal 8x8 chessboard in such a way that no white queen threatens a black queen (nor vice versa).
Or, phrasing the puzzle in a way parallel to Black and white queens on an 8x8 chessboard — changing only one word from that puzzle — I would say:
What is the largest number of queens that can be placed on a regular 8×8 chessboard, if the following rules are met:
- A queen can be either black or white, and there can be unequal numbers of each type [but if so, we count the smaller population].
- A queen must not be threatened by other queens of a different color.
- Queens threaten all squares in the same row, column, or diagonal (as in chess). Also, threats are blocked by other queens [not that this matters].
Can you find a way to place more than 8 queens of each color "peacefully" on an 8x8 chessboard?
geometry chess checkerboard
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$begingroup$
Based on the rules, why couldn't one place 64 white queens or 64 black queens?
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– Jiminion
2 days ago
1
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@Jiminion: Someone commented the same thing on puzzling.stackexchange.com/questions/28926/… ! :) I've edited that part of the question to reflect that if you place, e.g., 9 white queens and 7 black queens, your score is "7", not "9". And if you place 64 white queens and 0 black queens, your score is "0", not "64".
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– Quuxplusone
2 days ago
2
$begingroup$
Or, phrasing the puzzle another way, what is the continuation of this sequence? 0, 0, 1, 2, 4, 5, 7, 9, 12, 14, 17, 21, ... It turns out that this is OEIS sequence A250000 and fairly well studied! :)
$endgroup$
– Quuxplusone
2 days ago
add a comment |
$begingroup$
Here's a discrete variation of yesterday's puzzle Peaceful Encampments.
You have 8 white queens and 8 black queens. Place all these pieces onto a normal 8x8 chessboard in such a way that no white queen threatens a black queen (nor vice versa).
Or, phrasing the puzzle in a way parallel to Black and white queens on an 8x8 chessboard — changing only one word from that puzzle — I would say:
What is the largest number of queens that can be placed on a regular 8×8 chessboard, if the following rules are met:
- A queen can be either black or white, and there can be unequal numbers of each type [but if so, we count the smaller population].
- A queen must not be threatened by other queens of a different color.
- Queens threaten all squares in the same row, column, or diagonal (as in chess). Also, threats are blocked by other queens [not that this matters].
Can you find a way to place more than 8 queens of each color "peacefully" on an 8x8 chessboard?
geometry chess checkerboard
$endgroup$
Here's a discrete variation of yesterday's puzzle Peaceful Encampments.
You have 8 white queens and 8 black queens. Place all these pieces onto a normal 8x8 chessboard in such a way that no white queen threatens a black queen (nor vice versa).
Or, phrasing the puzzle in a way parallel to Black and white queens on an 8x8 chessboard — changing only one word from that puzzle — I would say:
What is the largest number of queens that can be placed on a regular 8×8 chessboard, if the following rules are met:
- A queen can be either black or white, and there can be unequal numbers of each type [but if so, we count the smaller population].
- A queen must not be threatened by other queens of a different color.
- Queens threaten all squares in the same row, column, or diagonal (as in chess). Also, threats are blocked by other queens [not that this matters].
Can you find a way to place more than 8 queens of each color "peacefully" on an 8x8 chessboard?
geometry chess checkerboard
geometry chess checkerboard
edited 2 days ago
Quuxplusone
asked 2 days ago
QuuxplusoneQuuxplusone
26317
26317
$begingroup$
Based on the rules, why couldn't one place 64 white queens or 64 black queens?
$endgroup$
– Jiminion
2 days ago
1
$begingroup$
@Jiminion: Someone commented the same thing on puzzling.stackexchange.com/questions/28926/… ! :) I've edited that part of the question to reflect that if you place, e.g., 9 white queens and 7 black queens, your score is "7", not "9". And if you place 64 white queens and 0 black queens, your score is "0", not "64".
$endgroup$
– Quuxplusone
2 days ago
2
$begingroup$
Or, phrasing the puzzle another way, what is the continuation of this sequence? 0, 0, 1, 2, 4, 5, 7, 9, 12, 14, 17, 21, ... It turns out that this is OEIS sequence A250000 and fairly well studied! :)
$endgroup$
– Quuxplusone
2 days ago
add a comment |
$begingroup$
Based on the rules, why couldn't one place 64 white queens or 64 black queens?
$endgroup$
– Jiminion
2 days ago
1
$begingroup$
@Jiminion: Someone commented the same thing on puzzling.stackexchange.com/questions/28926/… ! :) I've edited that part of the question to reflect that if you place, e.g., 9 white queens and 7 black queens, your score is "7", not "9". And if you place 64 white queens and 0 black queens, your score is "0", not "64".
$endgroup$
– Quuxplusone
2 days ago
2
$begingroup$
Or, phrasing the puzzle another way, what is the continuation of this sequence? 0, 0, 1, 2, 4, 5, 7, 9, 12, 14, 17, 21, ... It turns out that this is OEIS sequence A250000 and fairly well studied! :)
$endgroup$
– Quuxplusone
2 days ago
$begingroup$
Based on the rules, why couldn't one place 64 white queens or 64 black queens?
$endgroup$
– Jiminion
2 days ago
$begingroup$
Based on the rules, why couldn't one place 64 white queens or 64 black queens?
$endgroup$
– Jiminion
2 days ago
1
1
$begingroup$
@Jiminion: Someone commented the same thing on puzzling.stackexchange.com/questions/28926/… ! :) I've edited that part of the question to reflect that if you place, e.g., 9 white queens and 7 black queens, your score is "7", not "9". And if you place 64 white queens and 0 black queens, your score is "0", not "64".
$endgroup$
– Quuxplusone
2 days ago
$begingroup$
@Jiminion: Someone commented the same thing on puzzling.stackexchange.com/questions/28926/… ! :) I've edited that part of the question to reflect that if you place, e.g., 9 white queens and 7 black queens, your score is "7", not "9". And if you place 64 white queens and 0 black queens, your score is "0", not "64".
$endgroup$
– Quuxplusone
2 days ago
2
2
$begingroup$
Or, phrasing the puzzle another way, what is the continuation of this sequence? 0, 0, 1, 2, 4, 5, 7, 9, 12, 14, 17, 21, ... It turns out that this is OEIS sequence A250000 and fairly well studied! :)
$endgroup$
– Quuxplusone
2 days ago
$begingroup$
Or, phrasing the puzzle another way, what is the continuation of this sequence? 0, 0, 1, 2, 4, 5, 7, 9, 12, 14, 17, 21, ... It turns out that this is OEIS sequence A250000 and fairly well studied! :)
$endgroup$
– Quuxplusone
2 days ago
add a comment |
4 Answers
4
active
oldest
votes
$begingroup$
Nine queens of each color. Some variation is possible.
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Nice. Far more asymmetric than my "intended" solution!
$endgroup$
– Quuxplusone
2 days ago
add a comment |
$begingroup$
Here's 8 peaceful queens of each color:
After a lot of messing around, I snuck in a 9th white queen (black still at 8)
I'll keep looking for a way to do 9 for each side, but it may not be possible.
$endgroup$
add a comment |
$begingroup$
Can I claim Nine-and-a-half? :-)
You can replace either bishop with a tenth queen, but then the other bishop's square must remain empty.
$endgroup$
$begingroup$
Solution deserves upvote despite bishops attacks each other, better use knight or rook.
$endgroup$
– z100
yesterday
2
$begingroup$
@z100 The intention with the bishops was 'one or the other'
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– Daniel Mathias
yesterday
add a comment |
$begingroup$
I got 8 Black Queens and 10 White Queens:
Also 9 and 9:
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add a comment |
Your Answer
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4 Answers
4
active
oldest
votes
4 Answers
4
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Nine queens of each color. Some variation is possible.
$endgroup$
$begingroup$
Nice. Far more asymmetric than my "intended" solution!
$endgroup$
– Quuxplusone
2 days ago
add a comment |
$begingroup$
Nine queens of each color. Some variation is possible.
$endgroup$
$begingroup$
Nice. Far more asymmetric than my "intended" solution!
$endgroup$
– Quuxplusone
2 days ago
add a comment |
$begingroup$
Nine queens of each color. Some variation is possible.
$endgroup$
Nine queens of each color. Some variation is possible.
answered 2 days ago
Daniel MathiasDaniel Mathias
6336
6336
$begingroup$
Nice. Far more asymmetric than my "intended" solution!
$endgroup$
– Quuxplusone
2 days ago
add a comment |
$begingroup$
Nice. Far more asymmetric than my "intended" solution!
$endgroup$
– Quuxplusone
2 days ago
$begingroup$
Nice. Far more asymmetric than my "intended" solution!
$endgroup$
– Quuxplusone
2 days ago
$begingroup$
Nice. Far more asymmetric than my "intended" solution!
$endgroup$
– Quuxplusone
2 days ago
add a comment |
$begingroup$
Here's 8 peaceful queens of each color:
After a lot of messing around, I snuck in a 9th white queen (black still at 8)
I'll keep looking for a way to do 9 for each side, but it may not be possible.
$endgroup$
add a comment |
$begingroup$
Here's 8 peaceful queens of each color:
After a lot of messing around, I snuck in a 9th white queen (black still at 8)
I'll keep looking for a way to do 9 for each side, but it may not be possible.
$endgroup$
add a comment |
$begingroup$
Here's 8 peaceful queens of each color:
After a lot of messing around, I snuck in a 9th white queen (black still at 8)
I'll keep looking for a way to do 9 for each side, but it may not be possible.
$endgroup$
Here's 8 peaceful queens of each color:
After a lot of messing around, I snuck in a 9th white queen (black still at 8)
I'll keep looking for a way to do 9 for each side, but it may not be possible.
edited 2 days ago
answered 2 days ago
Excited RaichuExcited Raichu
6,42021066
6,42021066
add a comment |
add a comment |
$begingroup$
Can I claim Nine-and-a-half? :-)
You can replace either bishop with a tenth queen, but then the other bishop's square must remain empty.
$endgroup$
$begingroup$
Solution deserves upvote despite bishops attacks each other, better use knight or rook.
$endgroup$
– z100
yesterday
2
$begingroup$
@z100 The intention with the bishops was 'one or the other'
$endgroup$
– Daniel Mathias
yesterday
add a comment |
$begingroup$
Can I claim Nine-and-a-half? :-)
You can replace either bishop with a tenth queen, but then the other bishop's square must remain empty.
$endgroup$
$begingroup$
Solution deserves upvote despite bishops attacks each other, better use knight or rook.
$endgroup$
– z100
yesterday
2
$begingroup$
@z100 The intention with the bishops was 'one or the other'
$endgroup$
– Daniel Mathias
yesterday
add a comment |
$begingroup$
Can I claim Nine-and-a-half? :-)
You can replace either bishop with a tenth queen, but then the other bishop's square must remain empty.
$endgroup$
Can I claim Nine-and-a-half? :-)
You can replace either bishop with a tenth queen, but then the other bishop's square must remain empty.
answered yesterday
BassBass
28.4k469175
28.4k469175
$begingroup$
Solution deserves upvote despite bishops attacks each other, better use knight or rook.
$endgroup$
– z100
yesterday
2
$begingroup$
@z100 The intention with the bishops was 'one or the other'
$endgroup$
– Daniel Mathias
yesterday
add a comment |
$begingroup$
Solution deserves upvote despite bishops attacks each other, better use knight or rook.
$endgroup$
– z100
yesterday
2
$begingroup$
@z100 The intention with the bishops was 'one or the other'
$endgroup$
– Daniel Mathias
yesterday
$begingroup$
Solution deserves upvote despite bishops attacks each other, better use knight or rook.
$endgroup$
– z100
yesterday
$begingroup$
Solution deserves upvote despite bishops attacks each other, better use knight or rook.
$endgroup$
– z100
yesterday
2
2
$begingroup$
@z100 The intention with the bishops was 'one or the other'
$endgroup$
– Daniel Mathias
yesterday
$begingroup$
@z100 The intention with the bishops was 'one or the other'
$endgroup$
– Daniel Mathias
yesterday
add a comment |
$begingroup$
I got 8 Black Queens and 10 White Queens:
Also 9 and 9:
$endgroup$
add a comment |
$begingroup$
I got 8 Black Queens and 10 White Queens:
Also 9 and 9:
$endgroup$
add a comment |
$begingroup$
I got 8 Black Queens and 10 White Queens:
Also 9 and 9:
$endgroup$
I got 8 Black Queens and 10 White Queens:
Also 9 and 9:
edited yesterday
answered yesterday
Brandon_JBrandon_J
1,05825
1,05825
add a comment |
add a comment |
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$begingroup$
Based on the rules, why couldn't one place 64 white queens or 64 black queens?
$endgroup$
– Jiminion
2 days ago
1
$begingroup$
@Jiminion: Someone commented the same thing on puzzling.stackexchange.com/questions/28926/… ! :) I've edited that part of the question to reflect that if you place, e.g., 9 white queens and 7 black queens, your score is "7", not "9". And if you place 64 white queens and 0 black queens, your score is "0", not "64".
$endgroup$
– Quuxplusone
2 days ago
2
$begingroup$
Or, phrasing the puzzle another way, what is the continuation of this sequence? 0, 0, 1, 2, 4, 5, 7, 9, 12, 14, 17, 21, ... It turns out that this is OEIS sequence A250000 and fairly well studied! :)
$endgroup$
– Quuxplusone
2 days ago