# The 8 queens problem.

• Sam_math
• | May 12, 2009
• | 14418 views

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.

• 4 years ago

• 5 years ago

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

• 5 years ago

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

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

• 5 years ago

another website to play the eight queens!

• 6 years ago

nice :)

• 6 years ago

1.82  2.1204

• 6 years ago

1. = 82

• 6 years ago

1.64 2.414

• 6 years ago

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

• 6 years ago

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...

• 6 years ago

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...

• 6 years ago

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.

• 6 years ago

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.

• 6 years ago

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

• 7 years ago

good

• 7 years ago

Wow!

• 7 years ago

I'snt the black king checkmated already! It would be so cool to fill the board with queens! except for 3 squares!

• 7 years ago

Cool...

• 7 years ago

"It wont let me move any pieces"

It isnt a puzzle to solve... its just a diagram.

• 7 years ago

It wont let me move any pieces