Answers.Body: <p><strong>Yes, it can</strong></p>
  
  <p><a href="https://i.sstatic.net/Uj6gB.png" rel="noreferrer"><img src="https://i.sstatic.net/Uj6gB.png" alt="enter image description here"></a></p>
  
  <p>This particular <a href="https://en.wikipedia.org/wiki/Knight%27s_tour#History" rel="noreferrer">knight's tour</a> 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.</p>
  
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2018-08-20T15:42:05.310Z
Answers.Text: Except, what kind of sorcery is used from f3 to h7... a double-jump?! EDIT: Ah, it is actually a double jump.
Answers.UserDisplayName: PascalVKooten
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2018-08-20T20:48:09.097Z
Answers.Text: I suppose you can also make an _open_ knight's tour (i.e. not a cycle) that starts from b1 and terminates at g1?
Answers.UserDisplayName: Jeppe Stig Nielsen
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2018-08-21T07:39:23.970Z
Answers.Text: @JeppeStigNielsen yes, you can!
Answers.UserDisplayName: Aric
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2018-08-19T12:51:42.907Z
Answers.LastActivityDate: 2018-08-21T07:39:12.037Z
Answers.LastEditDate: 2018-08-21T07:39:12.037Z
Answers.UserDisplayName: Aric
Body: <p>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).</p>
  
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2018-08-19T17:15:27.500Z
Comments.Text: 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.
Comments.UserDisplayName: GreenMatt
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2018-08-19T17:21:56.970Z
Comments.Text: @GreenMatt you can't go back to the beginning unless the tour is a circle like in the answer.
Comments.UserDisplayName: DonQuiKong
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2018-08-19T17:30:58.983Z
Comments.Text: @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
Comments.UserDisplayName: GreenMatt
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2018-08-19T18:57:09.433Z
Comments.Text: @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
Comments.UserDisplayName: DonQuiKong
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2018-08-20T18:40:08.340Z
Comments.Text: @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.)
Comments.UserDisplayName: ispiro
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2018-08-20T19:19:14.217Z
Comments.Text: @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.
Comments.UserDisplayName: GreenMatt
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2018-08-20T19:38:40.360Z
Comments.Text: @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.
Comments.UserDisplayName: ispiro
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2018-08-20T20:08:56.033Z
Comments.Text: @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
Comments.UserDisplayName: GreenMatt
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2019-09-28T23:50:16.183Z
Comments.Text: A knight can reach any square from starting on any square.
Comments.UserDisplayName: Inertial Ignorance
Tags: <analysis><knights>
Title: Can a knight move through all squares from its original position?
ThreadText: # Can a knight move through all squares from its original position?
  
  (Asked by: username_0 on 2018-08-19)
  
  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).
  
  **Tags:** analysis, knights
  
  > **Comments:**
  > **username_1**: 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.  
  > **username_2**: @username_1 you can't go back to the beginning unless the tour is a circle like in the answer.  
  > **username_1**: @username_2: 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  
  > **username_2**: @username_1 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  
  > **username_3**: @username_1 Why did you agree with username_2? 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.)  
  > **username_1**: @username_3: 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.  
  > **username_3**: @username_1 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.  
  > **username_1**: @username_3: 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  
  > **username_4**: A knight can reach any square from starting on any square.  
  
  ---
  
  ## 1 answers
  
  ### Answer by username_5 on 2018-08-19. Score: 58
  
  **Yes, it can**
  
  [![enter image description here](https://i.sstatic.net/Uj6gB.png)](https://i.sstatic.net/Uj6gB.png)
  
  This particular [knight's tour](https://en.wikipedia.org/wiki/Knight%27s_tour#History) 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.
  
  > **Comments:**
  > **username_6**: Except, what kind of sorcery is used from f3 to h7... a double-jump?! EDIT: Ah, it is actually a double jump.  
  > **username_7**: I suppose you can also make an _open_ knight's tour (i.e. not a cycle) that starts from b1 and terminates at g1?  
  > **username_5**: @username_7 yes, you can!  
  
  ---
  
  