Questions tagged [knight-tours]
Use this tag to describe mathematics questions dealing with the knight's tour problem. A knight's tour is a series of legal knight moves in chess that visits all of the squares on the board exactly once.
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Prove that no closed knight's tour is possible on the $2 \times 2 \times 2 \times 2 \times 2 \times 2$ chessboard
Let $n,k \in \mathbb{N}-\{0,1\}$. The generalization of the closed knight's tour problem to higher dimensions asks to move a knight along the $n^k$ cells of a $n \times n \times \cdots \times n$ ...
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Open knight's tours on $n \times n \times \cdots \times n \subseteq \mathbb{Z}^k$ boards ($k \in \mathbb{N}-\{0,1\}$)
I would like to know under what conditions there exisits a (possibly open) knight's tour on a generic (hyper)cubic lattice $\{\{0,1,\ldots,n-1\} \times \{0,1,\ldots,n-1\} \times \cdots \times \{0,1,\...
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Possible positions of the knight after moving $n$ steps in Chessboard.
Problem
There is a knight on an infinite chessboard. After moving one step, there are $8$ possible positions, and after moving two steps, there are $33$ possible positions. The possible position after ...
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Tour of chess king
Consider lame chess king that can move only one cell left, down and diagonal upright. Consider square chess board.
Question: Can such a king visit all cells of a board (each cell only once) and end up ...
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How I can shortly prove that you can have a closed knight's tour on the 6x6 chessboard?
On the website, the explanation that a knight's tour on a $6\times6$ board is possible is the continued proof of around $1\frac{1}{2}$ pages! It will be great if one of you could provide a simple, ...
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Question about closed knight's tours for n x m chessboard
Is there a simple mathematical algorithm where you can get a CLOSED knight' tour on an n x m chessboard? I need a way to prove that it is mathematically possible or impossible to have a closed knight'...
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Can an $(a,b)$- knight reach a given point on an infinite chessboard? What moves are needed?
An $(a,b)$-knight is defined here: Can an $(a,b)$-knight reach every point on a chessboard?. Starting from a position $(x_0, y_0)$, it can basically move to $(x_0 + a, y_0 + b)$, $(x_0 + a, y_0 - b)$, ...
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Table-game problem that a bit looks like Knight's Tour problem
Given a table containing some instruction in each cell ($L$ - $U$ - $R$ - $D$ = Left - Up - Right - Down). The coefficient of the instruction means the number of steps (for example, $2L$ means you ...
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Does the existence of a knights tour depend on the initial position taken in any way?
Attempting to find solutions for a knights tour using basic bactracking algorithms and came across that most examples use one of the corners as the starting point, does the existence of the tour ...
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Chess Knight Distance
On an $a×a$ chess-board knight takes $n$ jumps from the bottom left to the bottom right and $m$ jumps from the bottom left to the upper right.
For $a=7$ are 4 steps necessary.
Is $a=7$ the only ...
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Knightwise “Nearness” By Number Of Moves Required
Given an otherwise empty $n\times n$ chessboard with a knight on one of the squares, define the “knight-closedness” of this board as the maximum possible length of a minimal knight route from one ...
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Show that, in a chessboard it is possible to traverse to any given square from another given square using a knight. [closed]
Show that, in a chessboard it is possible to traverse to any given square from another given square using a knight.
This was asked in a high school math competition.
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Minimum number of moves to reach a grid point by modified knight in variant chessboard
I apologize if this is not the right board to post this question. I am dealing with a computational question that extends the question posed in Minimum number of moves to reach a cell in a chessboard ...
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Is it possible to start with a knight at some corner of a chess board and reach the opposite corner passing once through all the squares?
Is it possible to start with a knight at some corner of a chessboard and reach the opposite corner passing once through all the squares?
The knight can reach the other corner or any square for that ...
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chess board knight distance
Is there a formula to compute the "knight distance" on an infinite board? i.e. how many step a knight need to move from (0,0) to any point (i,j)?
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