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I am currently investigating how the knight's tour problem differs when a general knight (m, n) is used instead of a traditional knight (2, 1), where m represents moving a number of squares along one axis and n represents the number of squares along the other. Right now I am just approaching this problem through simply examining various examples and it's more of a trial and error basis. I am trying to determine the similarities and differences between the two problems. I think there might be a more structured approach to this and if anyone could provide some insight it would be greatly appreciated. I have limited experience with programming which is something I have attempted to work with so if there are any experienced programmers here that could give me advice on how to approach this problem that would be great as well :)

Perpenderp
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  • The first two general knights I looked at are K(4, 1) and K(3, 2). I attempted to write some code to determine whether they have knight's tours on an 8x8 board but was unsuccessful. With regards to board size, I would simply like to look at the smallest square board cases where general knight K(m, n) has a knight's tour. If I can determine board sizes for which the general knights K(4, 1) or K(3, 2) have knight's tours I will be happy. – Perpenderp Feb 25 '18 at 01:20
  • Your general knight is usually called an $(m,n)$-leaper, a term that might be useful if you're searching for literature on the topic. – bof Feb 25 '18 at 01:36
  • What precisely do you mean when you say you were "unsuccessful"? You couldn't write the code, or you couldn't get it to compile, or it took too long to run, or something else? – saulspatz Feb 25 '18 at 02:33
  • Apparently, both the (4,1) and (3,2) problems have been solved by Knuth. https://arxiv.org/pdf/math/9411240.pdf – saulspatz Feb 25 '18 at 02:51
  • Unsuccessful as in it wouldn't compile. I actually ended up using some code from geeksforgeeks' solution to the knight's tour problem by trying to change the moves and board size but there is probably some other variable I neglected to change that caused the error. This is the link to the code: http://ide.geeksforgeeks.org/index.php – Perpenderp Feb 25 '18 at 05:50

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