Chess Queens
How many ways can you arrange eight queens on a chess board so that none of them could take any other?
-Matthew Lauser
-Matthew Lauser
Labels: SharedPuzzle
posted by Mr Fahrenheit at
10:26 AM
Monday, April 14, 2008
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12 Comments:
0 with 8 queens someone is going to hit someone no matter how you place them.
There is really only one i could figure out
I see the error in my ways... I put 8 queens on without any queens in jeopardy, thus there are eight ways you can do it. Start at any corner and lay out your queens from the starting queen so that they are in an knight attack away. You can do this from any of the four corners and there are two ways for each corner, thus eight solutions. When you place each queen, make sure they are a knight attack away and not in attack otherwise.
Keenan, does that not lead to two opposite corners threatening each other?
I've come up with 8 ways, based on this scheme:
a5, b1, c8, d6, e3, f7, g2, h4
Turn that scheme by 90°, 180°, 270° and you have a 4 ways, mirror the scheme along a middle line and turn it again, and you have 8 ways.
I've no prof these are the only ways, though.
Sorry, there are 92 ways to arrange them. Don't forget that each queen IS unique, even if they look the same. You can switch two of them and that would make another arrangement. Probably the best way to do this is use eight queens that look different.
Matthew Lauser
ok.. i think the spirit of the question does not mean rotating or flipping to multiply the answer.
So i'm going to say 2. (yes, rotating and flipping will multiply would provide more, but I don't count them).
This was possed to our High School Algebra class (26 years ago), and my solution was different from the one the teacher had, but both worked.
mo (above) has one, the one my teacher new of.. I came up with this one: A1, B5, C8, D6, E3, F7, G2, H4
What color are they? The riddle does not say. A white queen does not take a white queen, no matter where you put it.
I found this question somewhere where I was sure you would not have seen it. It said the answer was 92. I posted it just as it was.
And the color doesn't matter. Have you ever seen eight people playing on one board? It's assuming that any queen that could possibly be taken by another (regardless of it's color) is in danger.
Why do you guys have to be so complicated. Although you can specify 90 degreess and black and white these are only points of view and irrelevant to the question
The actual riddle asnwer is two. There is only two logical formations that can be presented on the board that will stop a queen from taking another queen. Doing 90 degreee turns etc do not present any other logical formaitons other than replicating from another line of sight
Regards, Alan
a third, in addition to mo's and euclid's brother's, is highly symmetrical and i think can best be described as two letter L's performing the sexual act 69. a friend challenged me to this problem earlier tonight and after i got it i checked to see if there were any others online. apparently he knows of another version that is different from these three that has a curve shape to it. we were going to look it up but there was tv to watch...
Actually, the correct answer is 12 combinations.
http://www.math.utah.edu/~alfeld/queens/all.gif
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