Answers.Body: <p>This is not possible.</p>
  <p>Proof: Consider all the possible configurations where there are 8 knights and 0 bishops and then see if it is possible to remove one knight and place two bishops on empty, unattacked squares.</p>
  <p>In the top left diagram only the knights on b1, b4, c1 and c4 can be replaced with bishops. But although you can replace one of these knights with a bishop you cannot place another bishop on the board because all the empty squares are attacked. Hence if you place 7 knights on the board then you can place at most one bishop. You can replace two knights with bishops but then you have only 6 knights and no more knights can be placed.</p>
  <p>Note that only with the top left and the rotated equivalent at the middle bottom can replace a knight with a bishop. In all the other cases replacing a knight with a bishop will leave a knight attacked.</p>
  <p><a href="https://i.sstatic.net/aBO7D.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/aBO7D.png" alt="enter image description here" /></a></p>
  <p>For this I found out possible combinations to have 8 unattacked knights and there were 6 (less than 6 if symmetry considered). Notice how each unoccupied square is attacked by 2 knights. So you are only free to remove 1 knight to occupy a bishop. But then you have no squares left for a 2nd bishop</p>
  
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Answers.CreationDate: 2022-03-16T21:14:31.730Z
Answers.Text: thanks for taking the time to edit and complete the answer
Answers.UserDisplayName: cmgchess
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Answers.Text: Why do you have to start with 8 **unattacked** knights? Why can't you start with 8 knights placed so that two of them attack each other? Of course you have to remove one of those two knights before looking for squares for the bishops.
Answers.UserDisplayName: bof
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Answers.Text: Maybe it would be easier to consider all ways of placing 2 nonattacking bishops, and observe that in each case the maximum number of knights that can be added is no more than 6. If I counted right, there are (considering symmetry) just 21 ways to place two bishops, and just 13 ways such that they don't attack each other.
Answers.UserDisplayName: bof
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Answers.CreationDate: 2022-03-17T08:41:42.737Z
Answers.Text: @bof i used a code snippet to generate all positions with 8 unattakced knights. after that only i tried the rest
Answers.UserDisplayName: cmgchess
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Answers.CreationDate: 2022-03-17T11:45:29.047Z
Answers.Text: How do you know you can start with 8 unattacked knights? Are you sure that every configuration of 7 unattacked knights can be obtained from one with 8 unattacked knights?
Answers.UserDisplayName: bof
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Answers.CreationDate: 2022-03-17T11:49:10.530Z
Answers.Text: 7 unattacked knights has to be a subset of this?  because when 8 unattacked knights placed, all the empty squares are attacked by more than 1 knight so to get 7 unattacked kngihts the only option is to remove a knight from 8 unattacked knights. that was the logic
Answers.UserDisplayName: cmgchess
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Answers.CreationDate: 2022-03-17T12:02:41.330Z
Answers.Text: You're saying that, given any set of 7 unattacked knights, you can always add one more unattacked knight. That seems to be true but not obvious.
Answers.UserDisplayName: bof
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Answers.UserDisplayName: cmgchess
Body: <p>How to place 2 bishops and 7 knights on a 4x4 chessboard without any of them attacking other pieces?</p>
  <p>There are no other restrictions.</p>
  
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2022-03-16T16:11:11.673Z
Comments.Text: is this possible
Comments.UserDisplayName: cmgchess
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Comments.CreationDate: 2022-03-16T16:33:21.847Z
Comments.Text: @cmgchess I was told that one student at my college solved it before7 years, but I doubt it.
Comments.UserDisplayName: Josip Maričević
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Comments.CreationDate: 2022-03-16T16:35:56.303Z
Comments.Text: i found this https://www.geeksforgeeks.org/place-k-knights-such-that-they-do-not-attack-each-other/ and from this can get board positons for 4*4 with 7 knights. see if you can more than 1 unattacked square for bishop
Comments.UserDisplayName: cmgchess
Tags: <puzzles>
Title: How to place certain pieces on a 4x4 chess board without any of them attacking each other?
ThreadText: # How to place certain pieces on a 4x4 chess board without any of them attacking each other?
  
  (Asked by: username_0 on 2022-03-16)
  
  How to place 2 bishops and 7 knights on a 4x4 chessboard without any of them attacking other pieces?
  
  There are no other restrictions.
  
  **Tags:** puzzles
  
  > **Comments:**
  > **username_1**: is this possible  
  > **username_0**: @username_1 I was told that one student at my college solved it before7 years, but I doubt it.  
  > **username_1**: i found this https://www.geeksforgeeks.org/place-k-knights-such-that-they-do-not-attack-each-other/ and from this can get board positons for 4*4 with 7 knights. see if you can more than 1 unattacked square for bishop  
  
  ---
  
  ## 1 answers
  
  ### Answer by username_1 on 2022-03-16. Score: 2
  
  This is not possible.
  
  Proof: Consider all the possible configurations where there are 8 knights and 0 bishops and then see if it is possible to remove one knight and place two bishops on empty, unattacked squares.
  
  In the top left diagram only the knights on b1, b4, c1 and c4 can be replaced with bishops. But although you can replace one of these knights with a bishop you cannot place another bishop on the board because all the empty squares are attacked. Hence if you place 7 knights on the board then you can place at most one bishop. You can replace two knights with bishops but then you have only 6 knights and no more knights can be placed.
  
  Note that only with the top left and the rotated equivalent at the middle bottom can replace a knight with a bishop. In all the other cases replacing a knight with a bishop will leave a knight attacked.
  
  [![enter image description here](https://i.sstatic.net/aBO7D.png)](https://i.sstatic.net/aBO7D.png)
  
  For this I found out possible combinations to have 8 unattacked knights and there were 6 (less than 6 if symmetry considered). Notice how each unoccupied square is attacked by 2 knights. So you are only free to remove 1 knight to occupy a bishop. But then you have no squares left for a 2nd bishop
  
  > **Comments:**
  > **username_1**: thanks for taking the time to edit and complete the answer  
  > **username_2**: Why do you have to start with 8 **unattacked** knights? Why can't you start with 8 knights placed so that two of them attack each other? Of course you have to remove one of those two knights before looking for squares for the bishops.  
  > **username_2**: Maybe it would be easier to consider all ways of placing 2 nonattacking bishops, and observe that in each case the maximum number of knights that can be added is no more than 6. If I counted right, there are (considering symmetry) just 21 ways to place two bishops, and just 13 ways such that they don't attack each other.  
  > **username_1**: @username_2 i used a code snippet to generate all positions with 8 unattakced knights. after that only i tried the rest  
  > **username_2**: How do you know you can start with 8 unattacked knights? Are you sure that every configuration of 7 unattacked knights can be obtained from one with 8 unattacked knights?  
  > **username_1**: 7 unattacked knights has to be a subset of this?  because when 8 unattacked knights placed, all the empty squares are attacked by more than 1 knight so to get 7 unattacked kngihts the only option is to remove a knight from 8 unattacked knights. that was the logic  
  > **username_2**: You're saying that, given any set of 7 unattacked knights, you can always add one more unattacked knight. That seems to be true but not obvious.  
  
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