8 Queens Problem

[Kehya]

I saw the problem in Training > General Training then click 8 Queen, I tried for ages. Can anyone come up with one set up? I think its impossible.

[Kevin Bonham]

I don't want to give this one away, because it's good practice to keep trying. It can be solved, I have one of the (many) solutions set up on a board in front of me.

Let me know if you get stuck and want a little hint.

[Kehya]

I understand its for training, though its just annoying not being able to solve it! ](*,)

[Sutek]

I understand its for training, though its just annoying not being able to solve it! ](*,)

There are 92 solutions, but only 12 which cannot be obtained the ones from the others by symmetry or rotation.

[hitman84]

place the queens at a7,b5,c3,d1,e6,f8,g2,h4

this is known as the famous n-queens problem the general algorithm is that
the 8 queens can be placed in 8*8 board,9 Q's in 9*9 board n so on
generalising n Q's on n*n board!

[Patrick Byrom]

place the queens at a7,b5,c3,d1,e6,f8,g2,h4

this is known as the famous n-queens problem the general algorithm is that the 8 queens can be placed in 8*8 board,9 Q's in 9*9 board n so on generalising n Q's on n*n board!

The general problem for n queens on an nxn board has now been solved:

If you have a few chess sets at home, try the following exercise: Arrange eight queens on a board so that none of them are attacking each other. If you succeed once, can you find a second arrangement? A third? How many are there?

This challenge is over 150 years old. It is the earliest version of a mathematical question called the n-queens problem whose solution Michael Simkin, a postdoctoral fellow at Harvard University’s Center of Mathematical Sciences and Applications, zeroed in on in a paper posted in July. Instead of placing eight queens on a standard 8-by-8 chessboard (where there are 92 different configurations that work), the problem asks how many ways there are to place n queens on an n-by-n board. This could be 23 queens on a 23-by-23 board — or 1,000 on a 1,000-by-1,000 board, or any number of queens on a board of the corresponding size.