Mathematician Answers Chess Problem About Attacking Queens:
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.
"It is very easy to explain to anyone," said Érika Roldán, a Marie Skłodowska-Curie fellow at the Technical University of Munich and the Swiss Federal Institute of Technology Lausanne.
Simkin proved that for huge chessboards with a large number of queens, there are approximately (0.143n)n configurations. So, on a million-by-million board, the number of ways to arrange 1 million non-threatening queens is around 1 followed by about 5 million zeros.
(Score: 0) by Anonymous Coward on Sunday September 26 2021, @07:00PM (9 children)
The pattern is flipped/mirrored and 90 degree rotation.
If they made the same mistake in their math. 1M x 1M would be 25 followed by 5M-1 zeros
(Score: 0) by Anonymous Coward on Sunday September 26 2021, @07:36PM
There are many mirror patterns. I've played with this and even wrote some very optimized code about 20 years ago. I must dust that off again now that CPUs are blazing fast, maybe add multi-core capability to it. It was seriously fun running it back then, and I was getting N up into the high 20s on a desktop.
(Score: 2) by vux984 on Sunday September 26 2021, @08:43PM (5 children)
No mistake. A reflection or rotation is a different configuration. It's an equivalent configuration, but its still a different arrangement, the queens are all on a different set of squares.
(Score: 1, Interesting) by Anonymous Coward on Sunday September 26 2021, @08:49PM (4 children)
(Score: 4, Insightful) by FatPhil on Sunday September 26 2021, @09:11PM (2 children)
The dining philosophers problem is nothing to do with philosophising. The busy beaver problem involves no rodents.
Great minds discuss ideas; average minds discuss events; small minds discuss people; the smallest discuss themselves
(Score: 1, Touché) by Anonymous Coward on Sunday September 26 2021, @10:22PM (1 child)
For example, there are only 3 possible openings corner, side, center … not the 9 most people guess. The travelling salesman is similarly affected. Doesn't matter the absolute compas direction, just the relative direction and distance between each point. So flipping the map, rotating it, or mirroring it makes no difference. Point A is still point A, and the distance to point B is still the same.
(Score: 2) by FatPhil on Monday September 27 2021, @04:46AM
Great minds discuss ideas; average minds discuss events; small minds discuss people; the smallest discuss themselves
(Score: 2) by vux984 on Monday September 27 2021, @01:03AM
Your not wrong about that.
Nevertheless suppose I were to ask you: "Given a chess board and one queen, how many places can you put that queen on the board so that it is in a corner?".
The board still has 4 corners, and even though all 4 solutions are symmetrical to the others, the correct answer is still 4.
(Score: 2) by FatPhil on Sunday September 26 2021, @09:05PM (1 child)
Up to symmetry, there are 12 unique solutions, not 23. Why? Because 92 = 88 + 4.
I win.
Great minds discuss ideas; average minds discuss events; small minds discuss people; the smallest discuss themselves
(Score: 1, Touché) by Anonymous Coward on Sunday September 26 2021, @10:43PM
You do have to appreciate pedantically calling out the mathematicians that study this problem by saying they didn't factor in reflective symmetry and rotational symmetry while simultaneously not factoring in reflective and rotational symmetry and missing that some solutions are symmetrical.
(Score: 2) by Opportunist on Sunday September 26 2021, @07:12PM (1 child)
What if you also introduce the additional rule that a queen can only move up to m spaces. Does that allow for more than n queens on an n*n field, and if, what relationship would m and n have to have?
(Score: 1, Interesting) by Anonymous Coward on Sunday September 26 2021, @10:50PM
There is a related Kings puzzle and other fairy pieces. But like many derivative/variant puzzles, they don't usually get the same amount of attention until the fundamental problem is "solved" or hits a dead end.
(Score: 2) by vux984 on Sunday September 26 2021, @08:28PM (3 children)
One chess set is fine. You need 8 pieces to represent 8 queens, the white pawns will do fine.
(Score: 3, Funny) by FatPhil on Sunday September 26 2021, @08:47PM (1 child)
Go players can go get bent, of course.
Great minds discuss ideas; average minds discuss events; small minds discuss people; the smallest discuss themselves
(Score: 0) by Anonymous Coward on Sunday September 26 2021, @11:56PM
Go players will be totally uninterested. Nothing move on the board, only in the mind of the players.
(Score: 0) by Anonymous Coward on Monday September 27 2021, @01:22AM
Hey now! Some of the black pawns might dig the transgender scene as well. Just sayin' ;-)
(Score: 1, Funny) by Anonymous Coward on Monday September 27 2021, @01:32AM (3 children)
It's that a hate crime now?
(Score: 0) by Anonymous Coward on Monday September 27 2021, @03:47AM (1 child)
Mate, you wouldn't last 30 seconds in Windsor Castle.
Liz II would deploy the battle corgies and you'd be toast. They look cute but they're deadly killing machines.
(Score: 0) by Anonymous Coward on Tuesday September 28 2021, @12:18AM
Put me in the Iron Maiden!
(Score: 0) by Anonymous Coward on Monday September 27 2021, @10:08PM
What kind of asshole is moderating this shit down??! Fuck you people! You're turning just as sour as those idiots at Slashdot! Go over there and bitch! Let us have our bit of fun
(Score: 2) by deimtee on Monday September 27 2021, @03:04AM (3 children)
Anyone want to bet that approximately 0.143 turns out to be approximately 0.142857142857 ?
If you cough while drinking cheap red wine it really cleans out your sinuses.
(Score: 0) by Anonymous Coward on Monday September 27 2021, @04:07PM (1 child)
You are suggesting that the solution involves 1/7.
I'm intrigued as to why THAT fraction. At first it made sense to be as 7=8-1 (that is after placing the first queen you now have 7 more to place). But since they were talking about the generalize case, that doesn't make any sense, it could be a matter of the number of directions that a queen can travel (8), but I'm just not convinced that that makes sense either.
(Score: 2) by deimtee on Tuesday September 28 2021, @04:42AM
Those were the two reasons I thought of too, but I had absolutely no backing for it. I was just intrigued that the constant was so close to 1/7 (while still being described as "approximately", which would give it enough wriggle room to be exactly 1/7).
If you cough while drinking cheap red wine it really cleans out your sinuses.
(Score: 0) by Anonymous Coward on Tuesday September 28 2021, @01:29AM
You can do the math yourself, if you'd like. Q(n)=((1±o(1))ne−α)n where α=1.942±3×10−3
(Score: 0, Troll) by Acabatag on Monday September 27 2021, @03:23AM (1 child)
There are only two queens on a chess board. Isn't chess an interesting enough game, with enough possibilities, that totally impossible scenarios need not be considered for discussion?
(Score: 2) by FatPhil on Monday September 27 2021, @05:04AM
Great minds discuss ideas; average minds discuss events; small minds discuss people; the smallest discuss themselves
(Score: -1, Offtopic) by Anonymous Coward on Monday September 27 2021, @05:23AM
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