Magic Knight Tour

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Magic Tour -- from Wolfram MathWorld

http://mathworld.wolfram.com/MagicTour.html

Aug 24, 2020 · The "most magic" knight's tour known on the board has main diagonal sums of 264 and 256 and is shown on the right (Francony 1882). Extensive histories of knight's magic tours are given by Murray (1951) and Jelliss. In all, there are a total of 140 distinct semimagic knight's tours on the board (Stertenbrink 2003).

Knight Tours - magic-squares.net

http://magic-squares.net/knighttours.htm

Order-8 Magic Knight Tour. News Flash! May 22, 2007. Awani Kumar announced by email the first two solutions to an order- 8 Magic Knight Tour. All rows, columns, pillars, and the 4 triagonals of this cube sum to 2052. This cube is simple magic with no included magic squares. The knight tour is re-entrant.

Semi-Magic Knight's Tours

https://mayhematics.com/t/mk.htm

The reverse numbering of a semimagic tour is also semimagic (and the same is true for quasimagic and near-magic tours). The question remains; are quasi-magic knight tours on boards 4m by (4n + 2) such as the 8×10 and 12×6 the best that can be achieved or are magic knight tours possible on at least some boards of these proportions?

Magic Knight's Tours - Mayhematics

https://www.mayhematics.com/t/mg.htm

Theorem 2: A magic knight's tour is only possible on a board with both sides even. Chequering the cells of the board white and black, it is a property of the knight that it always moves to a cell of different colour to that on which it stands. All the cells of one colour will …

[PDF] Magic Knight's Tours in Higher Dimensions Semantic ...

https://www.semanticscholar.org/paper/Magic-Knight's-Tours-in-Higher-Dimensions-Kumar/75e8a083e85e21855735c1964cf6992c89f8c107

A knight's tour on a board is a sequence of knight moves that visits each square exactly once. A knight's tour on a square board is called magic knight's tour if the sum of the numbers in each row and column is the same (magic constant). Knight's tour in higher dimensions (n > 3) is a new topic in the age-old world of knight's tours. In this paper, it has been proved that there can't be magic ...

Magic Knight's Tours in Higher Dimensions - NASA/ADS

https://ui.adsabs.harvard.edu/abs/2012arXiv1201.0458K/abstract

A knight's tour on a board is a sequence of knight moves that visits each square exactly once. A knight's tour on a square board is called magic knight's tour if the sum of the numbers in each row and column is the same (magic constant). Knight's tour in higher dimensions (n > 3) is a new topic in the age-old world of knight's tours. In this paper, it has been proved that there can't be magic ...

Computing Magic Knight Tours

http://magictour.free.fr/

A knight's tour a(,) is magic, iff all rows and columns of a(,) sum to (n*n+1)*n/2, the magic constant of the MKT. A knight's tour a(,) is called diagonally magic, iff it is magic and the two main diagonals sum to the magic constant too. This project showed that no diagonally magic knight tour …

Knights tour - LinkedIn SlideShare

https://www.slideshare.net/sasank123/knights-tour-44378823

Feb 07, 2015 · MAGIC KNIGHT’S TOUR The squares of the chess board are numbered in the order of the knight’s moves. Full magic knight’s tour: Each column, row, and diagonal must sum to the same number. Magic knight’s tour: Each column and row must sum to the same number. 24.

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