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.

Feel free to ask questions, send feedback and even point out mistakes. Great conversations start with just a single word. How to write better comments?
1. 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 : : :

This site uses Akismet to reduce spam. Learn how your comment data is processed.

## Free Online Calculus Text Books

Once I listed books on Algebra and Related Mathematics in this article, Since then I was receiving emails for few more related articles. I have tried to list almost all freely available Calculus texts. Here we go: Elementary Calculus : An approach using infinitesimals by H. J. Keisler Multivariable Calculus by Jim Herod and George Cain Calculus by Gilbert Strang…

## We are now using MathJax!

The very first trouble I faced, while moving the blog from WordPress.com hosting to WordPress.org, was due to a bug in WordPress’s OPML importer. The ‘importer’ messed up with all LaTeX equations on this site — just by deleting a single but very important string from all LaTeX codes. If you are really moving your WordPress content from one blog…

## Essential Steps of Problem Solving in Mathematical Sciences

Learning how to solve problems in mathematics is simply to know what to look for.   Mathematics problems often require established procedures. To become a problem solver, one must know What, When and How to apply them. To identify procedures, you have to be familiar with the different problem situations. You must also be good in gathering information, extracting strategies…

## Three Children, Two Friends and One Mathematical Puzzle

Two close friends, Robert and Thomas, met again after a gap of several years. Robert Said: I am now married and have three children. Thomas Said: That’s great! How old they are? Robert: Thomas! Guess it yourself with some clues provided by me. The product of the ages of my children is 36. Thomas: Hmm… Not so helpful clue. Can…

## Numbers – The Basic Introduction

If mathematics was a language, logic was the grammar, numbers should have been the alphabet. There are many types of numbers we use in mathematics, but at a broader aspect we may categorize them in two categories: 1. Countable Numbers 2. Uncountable Numbers The numbers which can be counted in nature are called Countable Numbers and the numbers which can…