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?