Questions tagged [chess]
Mathematical questions in one way or another related to the game of chess.
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Count arrangements with pairs of attacking kings [closed]
I have a $1\times n$ chessboard and $2$ pairs of kings in it. Both components of each pair of kings must be adjacent in the chessboard, that is, they must be attacking.
Now, I want to calculate the ...
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The $n$ queens problem with no three on a line
The $n$ queens problem asks if we can place $n$ queens on an $n\times n$ chessboard such that no two queens attack one another. For example, when $n=8$, here are two solutions (images taken from ...
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Exact calculation of n-queens solutions [closed]
I'm new to this forum, but I'm hoping this community can help me with some guidance on sharing and improving a mathematical solution that I've developed for the $n$-queens problem and $n$-queens ...
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Chess pieces metrics in higher dimensions
A couple of days ago, I was thinking about applying the knight (the well-known piece of chess) metric to any cubic lattice $\mathbb{N}^k$, $k \in \mathbb{N}-\{0,1\}$.
I suddenly realized that, from $k ...
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Strategy-stealing in chess
Is it proved that white can guarantee at least draw in chess?
A while ago I was told that it was proved using strategy-stealing, but I cannot find a reference.
Postscript. Please accept my apology ---...
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Number of open tours by a biased rook on a specific $f(n)\times 1$ board which end on a $k$-th cell from the right
We have a simple structure - biased rook of the two types.
Biased rook of the first kind which make open tours on a specific $f(n)\times 1$ board where $f(n) = \left\lfloor\log_2{2n}\right\rfloor + 1$ ...
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How many consecutive forced moves are possible in chess?
The question concerns chess. I call a move forced if, in a given position, is the unique move consistent with the rules of the game. I wonder what is the largest integer $n$ such that there exists a ...
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Limited rook moves
I have an algebra problem, that could be solved if I could answer the following combinatorial problem.
Let $S$ and $T$ be two nonempty sets. We think of $S\times T$ as the index set for the squares ...
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Does the Angel have to be really smart?
My question is about the computational complexity of the Angel's strategy in the Angels and Devils game, tl;dr does the Angel have a polynomial time strategy.
I'm a big Conway fan, so as you can ...
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Algebraic properties of graph of chess pieces
For the purpose of this question, a chess piece is the King, Queen, Rook, Bishop or Knight of the game of chess. To a chess piece is attached a graph which represents the legal moves it can make on an ...
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Knight's tour problem
It is known that on an infinite board, if all squares of the form $(ki,kj)$ are removed, $k$ even, $i,j\in\mathbf{Z}$, then there is no knight's tour due to unbalanced black and white squares.
My ...
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Complexity class of chess when simulated by a Turing machine [closed]
Suppose we simulate the game of chess with a Turing machine $M$ as follows:
The semi-infinite input tape of $M$ contains a sequence of symbols beginning in the first cell of the tape. Each symbol ...
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Does knight behave like a king in his infinite odyssey?
The Knight's Tour is a well-known mathematical chess problem. There is an extensive amount of research concerning this question in two/higher dimensional finite boards. Here, I would like to tackle ...
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Search strategy for Babson task in chess
I asked this on a computer chess forum (programmers hang out there, etc.) and got no substantive answers, which makes me think it's a research question. Whether it's sufficiently mathematical is ...
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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 ...