All Questions
9 questions
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Name for an easy combinatorial game
What is the name of the following combinatorial game:
Two players, moving in turn.
Positions: $0,1,2,\ldots$.
Moves: $n\longmapsto n-1$ or $n\longmapsto \lfloor n/2\rfloor$
if $n>0$.
No move for $0$...
- 17.9k
69
votes
7
answers
17k
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What is a chess piece mathematically?
Historically, the current "standard" set of chess pieces wasn't the only existing alternative or even the standard one. For instance, the famous Al-Suli's Diamond Problem (which remained ...
6
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0
answers
186
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Combinatorial game similar to Sprouts
Is there a name for the following combinatorial game? Is there a solution which player has a winning strategy?
Basically this game is "Sprouts without midpoints". One starts with $n$ points in the ...
- 5,482
3
votes
1
answer
337
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Minimal Birthdays
In combinatorial game theory: The birthday of a game is defined recursively as 1 plus the maximal birthday of its options, with the zero game having birthday 0.
Suppose we define the quasi-birthday ...
- 1,129
5
votes
0
answers
306
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Generalization of Sprague-Grundy Theorem
In my research on Combinatorial Game Theory, I used a certain theorem that is essentially a generalization of the Sprague-Grundy theorem. Because the result hinges too much on the work of others to be ...
- 1,129
1
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0
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168
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What is known about infinite diminished disjunctive compounds of loopfree partizan combinatorial games?
Background
Basic theories of loopy (normal-play) games which may go on forever under the usual disjunctive sum (the game ends when there are no moves available for you in any component on your turn) ...
- 613
3
votes
4
answers
2k
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A chess question of W.T. Tutte [closed]
In "Graph theory as I have known it", p.12, Knights Errant, the late Tutte mentions as an aside the chess question "Does either Black or White have a certain win from the initial ...
- 313
1
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0
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389
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Has anyone seen this version of ring toss (combinatorial object) before?
In reference to a
question on work of Westzynthius and another
question relating to Jacobsthal's function, I have formed a game which I immodestly call Paseman's Ring Toss. I hope that it has been ...
- 13k
3
votes
1
answer
1k
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Sprague-Grundy sequence for the ruler game
Consider the game "Ruler", which is defined as follows. We start with finitely many coins in a line. A move in this game consists of turning over any number of coins, but they must be consecutive, ...
- 14k