Peaceable Queens - Numberphile A Colorful Unsolved Problem - Numberphile 5 months 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)
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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.

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Comments 555 Comments

SuperPosition
7:08
Tim Jones
OEIS dubs get
Gianluca Tartaro
It sounds like this could actually be described as a floor function. The integers themselves don’t have a pattern that is too recognizable, but the example with 3x3 makes me think that a function describing this would come up with a value between 1 and 2, and because of the restrictions given, it has to be lowered to 1. Just some food for thought.
Patrick Riddell
For his problem at the end:
You could put the king in the corner, then put Queens everywhere except the vertical line, the horizontal line, and the diagonal line that intersect the king. That would be n^2 - (3n - 2) queens. That is n^2 being every spot on the board, and 3n - 2 being the 3 lines that intersect the king (the minus 2 is because you'll have counted the spot the king is on 3 times). You also slide the king along the border to get the same result. This equation only starts giving positive results when n is 4 or more since you can't have any Queens on a smaller board with a King.
Aerimis
This man has literally the most relaxing voice on Earth. I'm more interested in this than I've been in anything for years, and I'm falling asleep because of his voice.
Rick TaHeck
Hello is this ASMR
Micah Kirkpatrick
What about with imaginary Queens same rules for the imaginary queens but if an imaginary queen is on top of a real Queen they get reduced to a blank space and they can only attack other imaginary queens
Machai Arcanum
For that brilliant puzzle on queens and a king I think a possible answer for an n*n chess board, the number of queens is = (n^2)-4n. I may update this after a proper look.
(But probably won’t)
ulfy01
Rupaul approves this video.
SZ
As a chess lover, this was interesting to think about..
Leo179
28. Another way of saying 28 is 28, but I'm not sure that that's the right 28, maybe you want a different 28. 28?
X tech tips
He was in witcher 3 for that scroll quest..
FourthDerivative
Yass queen don't slay
Shlomo Sheikchilli
more like royal standoff
kira-lily marshall
The way this man talks about this with so much passion, he sounds like he's narrating a nature documentary
Google Screen Name
This is some 🔥 ASMR tbh
Aritro Chatterjee
Please like my comment, just for fun
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.
Add Reply

A Colorful Unsolved Problem - Numberphile Peaceable Queens - Numberphile 5 months ago   09:39

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

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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

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