I'm so confused about this. I googled it and read about knight's tours, however they all start from illegitimate positions. I want to know if a knight can move through all squares from its original position (e.g. b8, g8, b1, and g1).

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    If the knight lands on all squares in its tour, at some point it is going to hit each "original square". So take one of the tours you've seen, and use one of those original squares as the starting point and follow the tour from there. When you get to the "end", go back to the beginning until you get back to that original square you used as your starting point. – GreenMatt Aug 19 at 17:15
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    @GreenMatt you can't go back to the beginning unless the tour is a circle like in the answer. – DonQuiKong Aug 19 at 17:21
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    @DonQuiKong: Yes, I should have specified a "closed tour" when I typed that. The point still holds for such tours. Now, can you show me a knight's tour that actually moves in a circle? :-p – GreenMatt Aug 19 at 17:30
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    @GreenMatt sure, just take the one in the answer and zoom out ;). But there are open tours so you would have had to prove there is a closed one too – DonQuiKong Aug 19 at 18:57
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    @GreenMatt Why did you agree with DonQuiKong? Why would it matter if it's not a closed one? Couldn't it backtrack and get everywhere? (Not saying you're wrong. I just don't understand.) – ispiro Aug 20 at 18:40

Yes, it can

enter image description here

This particular knight's tour is closed, meaning that it starts and finishes in the same square. Therefore, the knight can start at any square on the board and finish on the same square, since it just starts at a different point along the cycle.

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    (image taken from Wikipedia?) – user17180 Aug 20 at 14:10
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    Except, what kind of sorcery is used from f3 to h7... a double-jump?! EDIT: Ah, it is actually a double jump. – PascalVKooten Aug 20 at 15:42
  • I suppose you can also make an open knight's tour (i.e. not a cycle) that starts from b1 and terminates at g1? – Jeppe Stig Nielsen Aug 20 at 20:48
  • @JeppeStigNielsen yes, you can! – Aric Aug 21 at 7:39

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