Chess Problems

  1. In how many ways can two queens, two rooks, one white bishop, one black bishop, and a knight be placed on a standard $ 8 \times 8$ chessboard so that every position on the board is under attack by at least one piece?
    Note: The color of a bishop refers to the color of the square on which it sits, not to the color of the piece.
  2. Can you attack every position on the board with fewer than seven pieces?

Solution

  1. Two ways as follow:
  2. No. (…and I’m not pretty sure about this No)

Improved chessboard images via this website using Creative Commons.

Excellent Reader, Good Orator and Bad Writer. Talk about WordPress, PHP and Mathematics. I develop & design web applications that are visually brilliant and mass-friendly. I can also design stunning graphics to support my web-apps & amazing logos to amaze people. I have worked with several companies & individuals to deliver satisfactory results.