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The 8 queens problem.

Submitted by Sam_math on Tue, 05/12/2009 at 9:16am.

The problem consists in place 8 queen in a chessboard, but neither queen is able to attack other queen.

I found this solution after 30 min, but don´t see it untill you solve the problem by yourself, totally are 12 unique solutions (92 counting rotations and relfections).

There is an algorithm to construct the solutions, many variants, the general case (to place n queens in a nxn board) if you are interested you can check the wikipedia http://en.wikipedia.org/wiki/Eight_queens_puzzle to learn more.

P.D. Ignore the kings, but in chess.com diagrams they always appear.

» posted in Fun & Trivia
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Comments:

by MithilGharat - 4 months ago
Mumbai India
Member Since: Jul 2011
Member Points: 77

i have written compute program to solvethis puzzle. it shows all thw 92 solutions. ha ha it took my 1 hour to find all 92 solutions

by DoorbellX - 5 months ago
Southeast of Tucson United States
Member Since: Aug 2011
Member Points: 51

by Darkflameninja - 9 months ago
Somewhere in the Big Wide World United States
Member Since: Mar 2011
Member Points: 35

Go on Coolmath.com and play the bridge puzzle. Kinda difficult.

by TheShoal12 - 13 months ago
United States
Member Since: Dec 2010
Member Points: 15

Awesome! I never thought about putting 8 queens with having them attack each other.

Also, summitwei, coolmath is the best math website ever!

by summitwei - 19 months ago
United States
Member Since: Nov 2009
Member Points: 237
by kaushikdr - 2 years ago
London United Kingdom
Member Since: Sep 2008
Member Points: 183

nice :)

by petey1 - 2 years ago
Sydney Australia
Member Since: Dec 2009
Member Points: 17

1.82  2.1204

by chaderoo2 - 2 years ago
United States
Member Since: Mar 2009
Member Points: 509

1. = 82

by TigerSneak1 - 2 years ago
Clinton, NJ United States
Member Since: Jun 2009
Member Points: 321

1.64 2.414

by Chess5413 - 2 years ago
Lahore Pakistan
Member Since: Aug 2009
Member Points: 5

I love it. You are really not only a good chess player but also a great mathematician. Cool! Fantastic! Marvelous!

by chess01fan - 2 years ago
Iloilo city Philippines
Member Since: Jul 2009
Member Points: 6

I got some math problems for you.. solve this:

1. (7-5x4) + (40+34)=          2. 400+6x3 - (40-26)=

 

I'm gonna be so happy if you answer it correctly...

by chess01fan - 2 years ago
Iloilo city Philippines
Member Since: Jul 2009
Member Points: 6

Yeah...good problem. I can't think anymore, I spent my energy in playing chess this evening.. No other things inside my head thanks to Abe4869, I knew what to tell you...thanks by the way I learned techniques...

by vitali_10 - 2 years ago
Jerusalem Israel
Member Since: Sep 2007
Member Points: 417

Thanks OBIT for the solution. By the way, about the maharajahs on the 10X10 chessboard- 7 of the moves between the pieces are called wizard's moves in omega chess terminology (another chess variant).

by OBIT - 2 years ago
Roswell United States
Member Since: Jun 2009
Member Points: 119

For the symmetrical solution, place the queens on a3, b5, c2, d8, e1, f7, g4, h6.  I found this by writing a computer program that generated the 92 solutions.   (As has already been pointed out, there are 12 if rotations and reflections are excluded.)

 

Here another interesting one, which I found by expanding the computer program: Imagine a piece that combines the moves of the queen and the knight.  Let's call this piece a "maharajah", as it is known in at least one chess variant.   It is possible to place 10 maharajahs on a 10x10 chessboard such that none of them are attacking each other.  What's more, there is only one distinct solution, and the solution is symmetrical!  The solution is (call the new files i and j): a3, b6, c9, d1, e4, f7, g10, h2, i5, j8.

by nicagui - 2 years ago
Afghanistan
Member Since: Jun 2009
Member Points: 2

This is another solution: Qf1, Qd2, Qb3, Qh4, Qe5, Qg6, Qa7, Qc8: The solution is to put first a queen in every row. then verify that any of the queens are in differents files. Finally you have to verify the diagonals: 4 black and 4 white.

by vitali_10 - 2 years ago
Jerusalem Israel
Member Since: Sep 2007
Member Points: 417

This is not good diagram  jonatz_elise for 7 queens because Qc6 & Qh1 are attacking each other and also Qe2 & Qe7.

by jonatz_elise - 2 years ago
Muntinlupa Philippines
Member Since: Feb 2009
Member Points: 101

Wow! I thought that there's no solution to that puzzle!!! Once my classmates are trying to solve that puzzle......not one of us solved it. Here is one of the diagrams that we only put 7 queens

by vitali_10 - 2 years ago
Jerusalem Israel
Member Since: Sep 2007
Member Points: 417

You say there are 12 solutions. Can you show the most simetrical one? It would be pretty.

by markus99 - 2 years ago
Canada
Member Since: Apr 2009
Member Points: 53

good

by punkyboy - 2 years ago
Tai Pei Taiwan
Member Since: Jun 2009
Member Points: 387

Wow!

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