# 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:

Improved chessboard images via this website using Creative Commons.

Gaurav Tiwari

A designer by profession, a mathematician by education but a Blogger by hobby. With an experience of over seven years with WordPress, PHP and CSS3, Gaurav is capable of doing almost anything related to these. Beyond that, He is a mathematics graduate & a civil service aspirant.

### No Responses

1. codemonkees says:

I have an example of 6 queens attacking every position on a chess board (pardon my bad ascii gfx):
: : : : : : Q :
: Q : : : : : :
: : : : : : : :
: : Q : : : : :
: : : : : Q : :
: : : Q : : : :
: : : : : : : :
: : : : Q : : :