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Questions tagged [chessboard]

Use this tag for questions about the board on which the game of chess is played.

A chessboard is the board on which the game of chess is played.

The board has a square shape with its side being divided into eight parts resulting in a total of sixty-four subdivisions whose colors alternate between two colors. Each subdivision of the board is called a square and receives a unique identification to be used in chess notation, which may be descriptive, algebraic, or numeric. Each horizontal array of squares is called a rank, each vertical array of squares is called a file, and each line of squares of the same color touching corner to corner is called a diagonal.

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Probability of completing a self-avoiding chessboard tour

Someone asked a question about self-avoiding random walks, and it made me think of the following: Consider a piece that starts at a corner of an ordinary $8 \times 8$ chessboard. At each turn, it moves one step, either up, down, left, or right,…
Brian Tung
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A variant of the Knight's tour problem

The knight's tour problem is a famous problem in chess and computer science which asks the following question: can we move the knight on an $n \ \times \ n$ chessboard such that it visits every square exactly once? The answer is yes iff $n\geq5$.…
MathematicsStudent1122
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Number of Chess Games Possible: Parity Discussion

Chess is an incredibly intricate game, offering an immense number of moves and combinations. Due to this complexity, determining the precise count of legal chess games poses a significant challenge. As of my knowledge, the total number of possible…
zero2infinity
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Greatest number of non-attacking moves that queens can make on an $n \times n$ chess board.

I'm trying to extend my OEIS sequence A275815: Maximum total number of possible moves that any number of queens of the same color can make on an $n \times n$ chessboard. I have computed the first five terms by brute force, and examples of each are…
Peter Kagey
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Prove that if 33 rooks are placed on a chessboard, at least five don't attack one another

The question asks to prove that when 33 rooks are placed on an $8 \times 8$ chessboard that there are a total of 5 rooks that aren't attacking each other. What I know: 64 squares Rooks attack in straight lines at least 1 row must have more than 5…
Fmonkey2001
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Prove that if fifteen bishops were placed on a chessboard, then at least two of them attack each other.

Prove that if fifteen bishops were placed on a chessboard, then at least two of them attack each other. I was wondering if the following method is correct? (I also feel like I cheated a bit, as if they asked me the minimum bishops needed instead…
hs_math_enjoyer
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A simple game on infinite chessboard

Player $A$ chooses two queens and an arbitrary finite number of bishops on $\infty \times \infty$ chessboard and places them wherever he/she wants. Then player $B$ chooses one knight and places him wherever he/she wants (but of course, knight cannot…
Grešnik
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On an infinitely large chessboard, in how many paths of length $10$ can a knight take and end up in its original position?

The knight is moved exactly $10$ times. A knight has $8$ possible ways to move once. So I believe there are $8^{10}= 2^{30} \sim 1$ billion permutations. How many in which the knight ends up on the same square?
cornelius
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Chess board problem

Is it possible to write the numbers 1, 2, ..., 25 on the square of a 5 by 5 chess board (one number per square) such that any two neighbouring numbers differ by at most 4? (Two numbers are neighbours if they are written on squares that share a…
BittersweetNostalgia
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Placing kings on a 6x6 board - who wins?

Two players alternate placing kings on a $6\times6$ chessboard, such that no two kings are allowed to attack each other (not even two kings placed by the same player). The last person who can place a king wins. Which player has a winning…
Akiva Weinberger
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Chess rook tour of 64 moves

Consider an $8\times8$ chessboard. Let the rook be placed on the square a1. Is it possible for the rook to make a tour of $64$ moves such that: the rook visits every square once, the rook visits every square, the rook begins and ends on the square…
user263286
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Representing graphs by an arrangement of chess rooks

Consider a potentially infinite chessboard on which a number of rooks has been placed, under the restriction that any 2x2 square containing at least 3 rooks must contain a 4th rook. This way, for every rook $x$ there is exactly one maximal rectangle…
Michał Zapała
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Is mate-in-$n$ problem for Trappist-1 undecidable?

Trappist-1 is a variant of infinite chess that has a piece called huygens which leaps any prime number of squares orthogonally. To actually implement this game, it should have decidable mate-in-$0$ (checkmate detection) and stalemate-in-$0$…
Ris
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Minimum number of dominoes on an $n \times n$ chessboard to prevent placement of another domino.

OEIS sequence A280984 (based on this Math Stack Exchange question) describes the minimum number of dominoes on an $n \times n$ chessboard to prevent placement of another domino. The sequence begins: 0, 2, 3, 6, 9, 12, 17, 22, 27, 34, 41, 48, 57,…
Peter Kagey
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Domino Tiling 8 x 8 grid proof

How can I prove that at least 8 dominoes are required to allow a placement to which no further domino can be added without two dominoes sharing an edge Any help will be appreciated. edit : For 9 * 9 grid this is the best solution :
Rumi
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