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View Full Version : 9 Queens of the same color on a chessboard

Lexan
03-09-2005, 04:56 AM
Do you know how to locate 9 Queens of the same color on a chessboard using the rules of the game?

Frank Walker
03-09-2005, 06:07 PM

Trent Parker
03-09-2005, 07:25 PM
Ease up Frank!

Lexan What do you mean?

There is a puzzle where you attempt to put 8 queens on the board where they are not on the same diagonal rank or file as any other queen....

There is a thread here somewhere already for that puzzle i believe......

pballard
05-09-2005, 05:07 PM
Ease up Frank!

Lexan What do you mean?

There is a puzzle where you attempt to put 8 queens on the board where they are not on the same diagonal rank or file as any other queen....

There is a thread here somewhere already for that puzzle i believe......

Perhaps he means is it possible to play a game in which BOTH players get 9 queens (because 9 queens on one side is trivial). The answer is yes.

Frank Walker
05-09-2005, 05:40 PM
I dont think so because check mat is imminent and the opposing king will be forced to take one of the queens

Kevin Bonham
05-09-2005, 07:03 PM
I dont think so because check mat is imminent and the opposing king will be forced to take one of the queens

Bill Gletsos
05-09-2005, 07:13 PM
The eight queens problem is well known where the object is to place 8 queens on a chess board such that no queen is on the same rank, file or diagonal as any other queen.

Now it is fairly obvious that this criteria cannot be met with 9 queens.

The 9 queens problem is to place nine queens and one pawn on a chessboard in such a way that queens don't attack each other

Rincewind
05-09-2005, 07:25 PM
The eight queens problem is well known where the object is to place 8 queens on a chess board such that no queen is on the same rank, file or diagonal as any other queen.

Now it is fairly obvious that this criteria cannot be met with 9 queens.

The 9 queens problem is to place nine queens and one pawn on a chessboard in such a way that queens don't attack each other

Anyone know the status of the problem of 9 queens on a 9x9 "chessboard"?

Bill Gletsos
05-09-2005, 07:31 PM
Anyone know the status of the problem of 9 queens on a 9x9 "chessboard"?352 total solutions, 46 unique.

Rincewind
05-09-2005, 07:34 PM
352 total solutions, 46 unique.

So solvable and not entirely trivial I assume. This was my first thought as what might be intended when seeing this thread.

Bill Gletsos
05-09-2005, 08:18 PM
15 queens on a 15x15 board has 2,279,184 solutions and 285,053 unique..

One interesting aspect is that for the 6 queens on a 6x6 board there is 1 unique solution and 4 total and which has less solutions than the 5 queens on a 5x5 board which as 2 unique and 10 total.

Rincewind
05-09-2005, 08:40 PM
15 queens on a 15x15 board has 2,279,184 solutions and 285,053 unique..

One interesting aspect is that for the 6 queens on a 6x6 board there is 1 unique solution and 4 total and which has less solutions than the 5 queens on a 5x5 board which as 2 unique and 10 total.

Yep I was looking at a similar problem at one stage (though the specifics escape me at the moment) and there was definitely two different types of problems one of odd and another for even sided chess boards. I would assume the number of solutions for x queens in an x by x chessboard (N(x)) to be such that

N(5) < N(7) < N(9) < ...
and
N(6) < N(8) < N(10) < ...

but that nothing can generally be said about the relationship between odd and even Ns.

Frank Walker
05-09-2005, 09:11 PM
Got me there

Rincewind
05-09-2005, 09:20 PM
NB I remembered the specifics. It was 9 bishops on a 9x9 chessboard. It was posted in the rec math thread here

http://chesschat.org/showpost.php?p=30124&postcount=179

RuyLopez
24-12-2005, 04:41 PM
Umm I think he means that two players are playing a real game (you control both of them) and you have to be able to promote 8 pawns (total 9 queens) and not checkmate the other colour. the 'same colour' bit is that either white or black must do this.

according to me the position is possible, but how to reach it?

so everyone get out their chessbase light!