user32248: How to place 2 bishops and 7 knights on a 4x4 chessboard without any of them attacking other pieces?
There are no other restrictions.

user23596: 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.

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

32248: <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>
 23596: <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.stack.imgur.com/aBO7D.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/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>
