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Non-crossing knight tours - Free
http://euler.free.fr/knight/
This variant has several names: "non-crossing knight's tour" or "uncrossed knight's tour". In his "Mathematical Circus", Martin Gardner presents this problem and explains that the 6x6 tour found by Yarbrough can be improved from 16 to 17 jumps, you can try to play with this link. Donald Knuth wrote a program to explore all boards upto 8*8.
Longest uncrossed knight's path - flyordie.com
http://www.flyordie.com/chess/uncrossed/
The longest uncrossed knight's path is a puzzle on a chess board, in which your task is to find the longest possible path of a knight (using standard chess knight moves) in such a way that the path does not intersect itself. The classic longest uncrossed knight's path problem can be extended to any board size (larger than 2). In this small game ...
Knight's Tour - LinkedIn SlideShare
https://www.slideshare.net/kelumkps/knights-tour
Sep 04, 2011 · Longest uncrossed knights path The problem is to find the longest path the knight can take on nxn board, such that the path does not intersect itself. 19. References “Knights tour” [Online].
Knight's tour - Wikipedia
https://en.wikipedia.org/wiki/Knight%27s_tour
The earliest known reference to the knight's tour problem dates back to the 9th century AD. In Rudraṭa's Kavyalankara (5.15), a Sanskrit work on Poetics, the pattern of a knight's tour on a half-board has been presented as an elaborate poetic figure (citra-alaṅkāra) called the turagapadabandha or 'arrangement in the steps of a horse'. The same verse in four lines of eight syllables each ...
Information on the n Knight's Tour Problem - UVic.ca
https://webhome.cs.uvic.ca/~cos/inf/misc/Knight.html
A related problem is that of finding the longest "uncrossed" knight's tour. For n = 3,4,5,6,7,8 the longest tours have length 2, 5, 10, 17, 24, 35. This is sequence Anum=A003192"> A003192 in Another related problem is that of finding the minimal number of knights needed to attack (or occupy) every square of an n by n board.
Non-crossing Knight Tour in 3-Dimension
https://arxiv.org/pdf/0803.4259.pdf
The problem of knight‟s tour on a square board is almost as old as the game itself but the non-crossing (or the non-intersecting) tour problem is a recent one. Here, the knight needs not to visit all the squares but care should be taken to find the longest path on a given board without visiting a square twice or crossing its own path.
Knight Pattern - Chessprogramming wiki
https://www.chessprogramming.org/Knight_Pattern
Longest uncrossed knight's path from Wikipedia László Lindner's knight wheel by Frederic Friedel from ChessBase Puzzle Knight's Tour from Research Reflections by Graham Kendall , …
Longest path problem - Wikipedia
https://en.wikipedia.org/wiki/Longest_path_problem
NP-hardness. The NP-hardness of the unweighted longest path problem can be shown using a reduction from the Hamiltonian path problem: a graph G has a Hamiltonian path if and only if its longest path has length n − 1, where n is the number of vertices in G.Because the Hamiltonian path problem is NP-complete, this reduction shows that the decision version of the longest path problem is also NP ...
The Knight's tour problem Backtracking-1 - GeeksforGeeks
https://www.geeksforgeeks.org/the-knights-tour-problem-backtracking-1/
May 29, 2020 · Backtracking Algorithm for Knight’s tour Following is the Backtracking algorithm for Knight’s tour problem. If all squares are visited print the solution Else a) Add one of the next moves to solution vector and recursively check if this move leads to a solution. (A Knight …
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