All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > General
Mutually disagreeing queens. (Posted on 2006-05-19) Difficulty: 2 of 5
In how many ways can two queens be placed on a chessboard such that they are mutually attacking each other?

Show how to solve this problem quickly with only pencil and paper (not even a calculator).

No Solution Yet Submitted by Jer    
Rating: 4.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution Another solution | Comment 3 of 5 |
Consider the 4 squares like a1, or the 8 squares like a2, or the 8 like a3, or the 8 like a4: the other queen may be in 21 places --> 28x21=588.

For the 4 squares like b2, or the 8 like b3, or the 8 like b4, the other queen may be in 23 places --> 20x23=460.

For the 4 squares like c3, or the 8 like c4, the other queen may be in 25 places --> 12x25=300.

For the 4 squares like d4, the other queen may be in 27 places --> 4x27=108.

The total number of possibilities, if the queens were of different color, would be 1456; if they are the same color, halve this to get 728.

  Posted by Federico Kereki on 2006-05-19 11:03:03
Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (8)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2017 by Animus Pactum Consulting. All rights reserved. Privacy Information