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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).

Aric
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Huy Mai
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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 '18 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 '18 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 '18 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 '18 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 '18 at 18:40
  • @ispiro: If it is an open tour, then the tour does NOT cycle back to (one move away from) its beginning. Thus, unless the open tour starts on one of the "beginning squares" you will reach a point where there are no moves available, but there are still squares on the board the knight has not visited. – GreenMatt Aug 20 '18 at 19:19
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    @GreenMatt You're assuming move through all squares from its original position also means without visiting the same square twice (which I don't). So it's just two interpretations of the requirements. That's fine. – ispiro Aug 20 '18 at 19:38
  • @ispiro: The generally accepted definition of a knight's tour is that the knight visits each square on the board exactly once: https://en.wikipedia.org/wiki/Knight%27s_tour – GreenMatt Aug 20 '18 at 20:08
  • A knight can reach any square from starting on any square. – Inertial Ignorance Sep 28 '19 at 23:50

1 Answers1

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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.

Aric
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