Combinatorial game theory | Pursuit–evasion
The angel problem is a question in combinatorial game theory proposed by John Horton Conway. The game is commonly referred to as the Angels and Devils game. The game is played by two players called the angel and the devil. It is played on an infinite chessboard (or equivalently the points of a 2D lattice). The angel has a power k (a natural number 1 or higher), specified before the game starts. The board starts empty with the angel in one square. On each turn, the angel jumps to a different empty square which could be reached by at most k moves of a chess king, i.e. the distance from the starting square is at most k in the infinity norm. The devil, on its turn, may add a block on any single square not containing the angel. The angel may leap over blocked squares, but cannot land on them. The devil wins if the angel is unable to move. The angel wins by surviving indefinitely. The angel problem is: can an angel with high enough power win? There must exist a winning strategy for one of the players. If the devil can force a win then it can do so in a finite number of moves. If the devil cannot force a win then there is always an action that the angel can take to avoid losing and a winning strategy for it is always to pick such a move. More abstractly, the "pay-off set" (i.e., the set of all plays in which the angel wins) is a closed set (in the natural topology on the set of all plays), and it is known that such games are determined. Of course, for any infinite game, if player 2 doesn't have a winning strategy, player 1 can always pick a move that leads to a position where player 2 doesn't have a winning strategy, but in some games, simply playing forever doesn't confer a win to player 1, so undetermined games may exist. Conway offered a reward for a general solution to this problem ($100 for a winning strategy for an angel of sufficiently high power, and $1000 for a proof that the devil can win irrespective of the angel's power). Progress was made first in higher dimensions. In late 2006, the original problem was solved when independent proofs appeared, showing that an angel can win. Bowditch proved that a 4-angel (that is, an angel with power k = 4) can win and Máthé and Kloster gave proofs that a 2-angel can win. (Wikipedia).
When you FINALLY get the courage to perform a Magic Trick!
*Awkward silence
From playlist Magician Problems.
This WON'T Fool you... UNLESS you're a Magician!
*** HIT THE NOTIFICATION BUTTON SO YOU’LL NEVER MISS A VIDEO*** MAKE SURE YOU SUBSCRIBE AND LEAVE A COMMENT IF YOU WANT TO SEE MORE VIDEOS SUBSCRIBE HERE: https://www.youtube.com/CHRISRAMSAY52 Some light-hearted fun for the magicians out there. ;)
From playlist Magician Problems.
Why You Think You Might Have ADHD
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In this talk, we will define elliptic curves and, more importantly, we will try to motivate why they are central to modern number theory. Elliptic curves are ubiquitous not only in number theory, but also in algebraic geometry, complex analysis, cryptography, physics, and beyond. They were
From playlist An Introduction to the Arithmetic of Elliptic Curves
The Challenges of Anxious-Avoidant Relationships
Some of the most difficult relationships are those between people who can be categorised as 'avoidant' and others who are labelled 'anxious.' Learn to know which of these two you might be - and how better to handle the tensions that arise in a pairing with your counterpart. Sign up to our
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The corner cube problem is interesting because it initially looks difficult. When the problem was first posed to me, for example, it didn't know how to solve it. Still, my intuition bells were ringing, telling me there was a nice solution. In this video, I cover two of these solutions, in
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If you’re online, you may notice that conversations around ADHD are everywhere. You may even be starting to wonder, as you flick from one app to the next, that you yourself may have ADHD. So in Part 1 of this series about ADHD, Julian explores what this disorder is, what’s happening in the
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The Angel Problem [Game Theory]
A fascinating Game Theory problem proposed by John Conway. Original Paper: http://library.msri.org/books/Book29/files/conway.pdf 2-Angel Proof: http://homepages.warwick.ac.uk/~masibe/angel-mathe.nov10.pdf Music: Bass Loop - Wooseong https://soundcloud.com/wooseong012
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(October 9, 2009) Ras Bodik, from UC Berkeley Computer Science, discusses how partial programs can communicate programmer insight, how suitable synthesis algorithm completes the mechanics, and how end-user programming may be decomposable into partial program completion. Stanford Univers
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Angels Hastening: The Karbalāʾ Dreams - Christopher Clohessy
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The rules for how to doom a relationship are relatively easy to follow. Here are a selection that are guaranteed to blow up love. Please subscribe here: http://tinyurl.com/o28mut7 If you like our films take a look at our shop (we ship worldwide): http://www.theschooloflife.com/shop/all/ B
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Papers unpicked: Strategy on an Infinite Chessboard between an Angel and a Devil
This video discusses András Máthé's 2006 solution to the famous Angel problem, first described by John Conway in 1982. I encourage viewers to pause if needed, as this proof makes a fair few sharp turns and mental leaps that can take time to appreciate! The Angel problem went unsolved for
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Why Los Angeles won't run out of water: The Aqueduct - IT'S HISTORY
If you need help falling asleep, check out Endel. The first 100 people to download Endel at https://app.adjust.com/b8wxub6?campaign=itshistory_february&adgroup=youtube will get a free week of audio experience. Second only to the Panama Canal, the Los Angeles Aqueduct was once the most ext
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San Andreas Fault and the Complex Infrastructure of Los Angeles - D. Asimaki - 4/29/2016
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Do Angels and Demons Exist? | Episode 410 | Closer To Truth
Many theologians take angels and demons seriously. Why? Certainly, most human beings believe in angels and demons. Certainly, such nonphysical beings, in one form or another, populate most of the world's religions. Featuring interviews with J.P. Moreland, Thomas Flint, Dean Radin, Walter S
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