Sunday, January 20, 2019

geometry - Discrete Peaceful Encampments: 9 queens on a chessboard


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:



  1. 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].

  2. A queen must not be threatened by other queens of a different color.

  3. 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?




Answer



Can I claim Nine-and-a-half? :-)



enter image description here



You can replace either bishop with a tenth queen, but then the other bishop's square must remain empty.


No comments:

Post a Comment

classical mechanics - Moment of a force about a given axis (Torque) - Scalar or vectorial?

I am studying Statics and saw that: The moment of a force about a given axis (or Torque) is defined by the equation: $M_X = (\vec r \times \...