mathematics - Black and white queens on an 8x8 chessboard

What is the largest number of queens that can be placed on a regular $8\times8$ chessboard, if the following rules are met:

1. A queen can be either black or white, and there can be unequal numbers of each type.


2. A queen must not be threatened by other queens of the same color.


3. Queens threaten all squares in the same row, column, or diagonal (as in chess). Also, threats are blocked by other queens.

Bonus:

Would this number change if rule 1 was changed to enforce equal numbers of black and white queens?

Answer

I'll guess

32 queens.

Every other row is filled with alternating queens. Starting queens on each filled row alternate.

W B W B W B W B
- - - - - - - -
B W B W B W B W
- - - - - - - -
W B W B W B W B
- - - - - - - -

B W B W B W B W

I think this is ideal, since for a single queen, cutting off all lines of sight would require:

B - B - B
- - - - -
- B W B -
- - - - -
B - B - B

Filling white queens into the spaces and repeating the pattern gives us the 32 solution.