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Peaceable Queens - Numberphile | A Colorful Unsolved Problem - Numberphile - At Up-Tube.com

Peaceable Queens - Numberphile A Colorful Unsolved Problem - Numberphile 1 day ago   07:21

Numberphile
Neil Sloane discusses peaceable queens and chess. Check out Brilliant (get 20% off their premium service): https://brilliant.org/numberphile (sponsor)
More links & stuff in full description below ↓↓↓

Learn more at the OEIS entry (loads of links): https://oeis.org/A250000

References:
Ainley, Stephen. Mathematical Puzzles. London: G Bell & Sons, 1977.
Yukun Yao and Doron Zeilberger, Numerical and Symbolic Studies of the Peaceable Queens Problem, https://arxiv.org/abs/1902.05886

Other notable work by Michael De Vlieger, Benoit Jubin, Peter Karpov, Don Knuth, Rob Pratt, Bob Selcoe, Paul Tabatabai.

More Numberphile videos with Neil Sloane: http://bit.ly/Sloane_Numberphile

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Comments 555 Comments

Felix T-Rex
handsome man
Bjamse
ok, but is there a relationship between the player who has to make the first move in any of these positions and the player who wins?
Perfect_Poop
Segregation at its finest.
Yav Tomar
What's the answer for tree(3)
Tyler Young
Er... maybe you should take up quantum computation and utilize destructive interference to figure the sequence...
jamma246
The king + queens problem seems super obvious to me... Choose the position of the king first. The number of queens you can place is equal to the number of spaces on the board (64) minus the number of squares on rows, columns and diagonals that hit that square, since you can place a queen on everything except such squares. Every square has 15 squares on rows and columns hitting that square. It's easy to check that you get at least another 7 from diagonals, minimised by placing the king on the edge of the board. So the answer is 64-15-7 =




:O
Francis Luglio
I want a video on those 28s
Mujahid Syed
Literally any chess piece: *exists
Queen: "Get nae-nae'd"
Thomas Busse
I'm wondering ... why does Sloane come on every time the news gets really weird? Last year, we had the palendromic zip code thing in California, and now the news is all based on Star Trek IV and Kabbalah.
Anthony Nguyen
These are super basic assumptions I created to find some permutations..although these are 100% wonky

1. We require for n amounts of Queens to be placed on the board, but there must n amounts of spaces left over.
2. We can cut down the brute force by saying if(there is a queen on each row){go onto the next sequence}
3. Of course, we will save that sequence in case it becomes a Parent sequence to sequences with higher N's. For instance, we might use N = 24 for an 18x18. But after we compute that, we go onto N=25 and happen to find a sequence that matches a sequence in N=24.
4. We can cut it down even more by saying if(there is a queen on each column){go onto next sequence}
5. We can cut it down even more by saying if(there is a queen on a whole diagonal){go onto next sequence}; although, we can generalize this even more by saying if(there is a queen on half or greater than half of the BOTH diagonals){go onto next sequence}
6. We can cut it down even more by saying if(queens >= area of chessboard){Next chessboard size}
Louis Mendes
his studio room is utterly fabulous.
Reinis Martinsons
0:07 that queen would get taken by the pawn
cream bun
This was one of the puzzles of the game 7th Guest.
Lordious
Too shortttttttttt
Winston Churchill
"Chess Queens are a trained warrior. They are trained to attack."
*sees queen captured by other queen*
headshiphero
More Neil Sloane videos please! Not only is here the founder of the OEIS, but he also has a lovely relaxing voice :)
Alexander Thompson
This guy needs to narrate an audio book.
Astralknight532
So basically, the 8 queens problem I was given in my 1st year computer science class (as homework to program in Java). That's what I guessed when I saw the video title, except that this is more general so that it works for any even number of queens and the necessary size of chess board to fit the queens on it.
Ping Pong Cup Shots
Why is everybody suddenly talking about the 301 video?
UnknownRager96
Bonus puzzle solution:
The top-left corner (works for any corner) can be attacked from any queens in the colunm, row, and diagonal of the king, and placing the queens at the other spots leaves 1 king, 21 empty spots and 42 (wow) queens.
For an n x n board, just put it in the corner and do the Sam thing as an 8 x 8 board
Add Reply

A Colorful Unsolved Problem - Numberphile Peaceable Queens - Numberphile 1 day ago   10:15

James Grime on the Hadwiger–Nelson problem.
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Extra footage from this interview: https://up-tube.com/upvideo/7aOgEXiHbk4

The Four Color Map Theorem: https://up-tube.com/upvideo/AtoX43wO4eD

More on James Grime (you can book him for talks): http://singingbanana.com

More James Grime videos: http://bit.ly/grimevideos

The de Grey paper: https://arxiv.org/abs/1804.02385

A good write up on this topic via Quanta Magazine: https://www.quantamagazine.org/decades-old-graph-problem-yields-to-amateur-mathematician-20180417/

The Marijn Heule counterexample: http://www.cs.utexas.edu/users/marijn/CNP/553.png

More links & stuff in full description below ↓↓↓

Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): http://bit.ly/MSRINumberphile

We are also supported by Science Sandbox, a Simons Foundation initiative dedicated to engaging everyone with the process of science. https://www.simonsfoundation.org/outreach/science-sandbox/

And support from Math For America - https://www.mathforamerica.org/

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