Let's Play Some Chess-1

By using the formula for calculating the number of bishops such that they do not attack each other,that is 2n-2,we arrive at the answer 14.

Note that no two bishops can attack each other if they are present on different colored squares. Therefore, the maximum number of bishops that can be placed on black squares is equal to the maximum number of bishops satisfying the given condition that can be placed on white squares.

So let us count the maximum number of bishops that are present on black squares.

It is easy to see that all the diagonals that are parallel to the main black diagonal are 7 (including the main diagonal). Note that every diagonal can contain at most one bishop. Thus the number of bishops that can be placed on black squares is $\leq$ 7.

Now, we give a construction to show that the extreme case (7 bishops) is possible.

This can be done by placing 4 bishops on the 1st column and 3 on the 8th one.

$\Rightarrow$ The maximum number of bishops that can be placed on black squares and satisfying the given condition is 7 and therefore, the required answer is $7×2=14$