Answers.Body: <p>The furthest distance is from one corner to the opposite one.  You can get from a1 to h8 in six moves, for example a1,c2,d4,f3,e5,g6,h8.  There are few pairs of squares that take more than four moves.</p>
  
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Answers.CreationDate: 2014-01-16T19:44:21.327Z
Answers.LastActivityDate: 2014-01-16T19:44:21.327Z
Answers.UserDisplayName: Ross Millikan
Answers.Body: <p>N can be infinite.  I can always make a zillion knight moves.  So I expect you really want to know the smallest number of moves a Knight needs to get from square A to square B.</p>
  
  <p>Some N's won't work.  A Knight on a1 can't get to b3 in any even number of moves.</p>
  
  <p>One thing we know - if the start and end squares are the same color, it will take an even number of moves.  If they are different colors, it will take an odd number of moves.</p>
  
  <p>It doesn't take long to figure out the longest path on the board (a8 to h1 for example) requires six moves. Note the start and end squares are the same color.  For alternating colors, the requirement is 5 moves, max.</p>
  
  <p>I don't think there will be an equation where one enters the square locations and a single number comes out.</p>
  
Answers.ContentLicense: CC BY-SA 3.0
Answers.CreationDate: 2014-01-13T09:21:25.183Z
Answers.Text: I think "he _has_ to move N moves. how big could N be?" means that the question is about the smallest number.
Answers.UserDisplayName: JiK
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Answers.CreationDate: 2014-01-13T09:58:58.733Z
Answers.Text: The question is indeed about the smallest number
Answers.UserDisplayName: Lynob
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Answers.UserDisplayName: Tony Ennis
Answers.Body: <p>If the knight cannot touch the same square twice then the answer is 63. See <a href="http://en.wikipedia.org/wiki/Knight%27s_tour" rel="nofollow">Knight's tour</a></p>
  
  <p>A coworker of mine wrote the software to determine the route a long time ago.</p>
  
Answers.ContentLicense: CC BY-SA 3.0
Answers.CreationDate: 2014-09-02T12:49:16.497Z
Answers.Text: may i take a look at the software source code? or is it not open source?
Answers.UserDisplayName: Lynob
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Answers.CreationDate: 2014-09-02T13:15:56.043Z
Answers.Text: Sadly, it is not.
Answers.UserDisplayName: ZL1Corvette
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Answers.CreationDate: 2014-09-02T12:46:48.890Z
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Answers.UserDisplayName: ZL1Corvette
Answers.Body: <p>I think the options are finites (not infinite) is possible calculate all the possible moves from f3 to g8 so the Knight can take the Bishop but its a longest number.</p>
  
  <p>Since the chess board is finite in dimensions (8x8) all the possible moves can be calculated, but off course it will be again a very longest number.</p>
  
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Answers.UserDisplayName: mlacunza
Body: <p>Suppose the knight is on square X and he wants to get to square Y, and in order to do that he has to move N moves. how big could N be?</p>
  
  <p>Could that be solved using a mathematical equation? Say Nf3 should capture Bg8, could that be solved mathematically without having to take a look and analyze it step by step? is there an equation?</p>
  
Comments.ContentLicense: CC BY-SA 3.0
Comments.CreationDate: 2014-01-16T23:44:39.277Z
Comments.Text: This question doesn't seem quite complete. Do you mean the largest number of moves without ever occupying the same space? or without making the same exact move (between two spaces) twice? Otherwise Tony's right.
Comments.UserDisplayName: Partial Observer
Comments.ContentLicense: CC BY-SA 3.0
Comments.CreationDate: 2014-01-17T00:07:18.013Z
Comments.Text: No without making the same move twice, shortest path. Otherwise the number is obviously infinite and my question is nonsense
Comments.UserDisplayName: Lynob
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Comments.CreationDate: 2014-01-17T17:22:18.013Z
Comments.Text: @RauanSagit I want to see if chess could be solved mathematically, using equations
Comments.UserDisplayName: Lynob
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Comments.CreationDate: 2014-03-18T14:37:41.417Z
Comments.Text: The question is solved for arbitrary boards: http://books.google.de/books?id=QxX2CX5OVMsC&pg=PA337&lpg=PA337&dq=knight+metric&source=bl&ots=3J5nDWweOY&sig=_-pQwRWZrh0fI9SHzmkxlCb-Xcc&hl=de&sa=X&ei=-FkoU6WaLen8ywOjgoHoDg&ved=0CDIQ6AEwAA
Comments.UserDisplayName: chaosflaws
Tags: <theory><knights><mathematics>
Title: Longest path for knight
ThreadText: # Longest path for knight
  
  (Asked by: username_0 on 2014-01-13)
  
  Suppose the knight is on square X and he wants to get to square Y, and in order to do that he has to move N moves. how big could N be?
  
  Could that be solved using a mathematical equation? Say Nf3 should capture Bg8, could that be solved mathematically without having to take a look and analyze it step by step? is there an equation?
  
  **Tags:** theory, knights, mathematics
  
  > **Comments:**
  > **username_1**: This question doesn't seem quite complete. Do you mean the largest number of moves without ever occupying the same space? or without making the same exact move (between two spaces) twice? Otherwise username_4's right.  
  > **username_0**: No without making the same move twice, shortest path. Otherwise the number is obviously infinite and my question is nonsense  
  > **username_0**: @RauanSagit I want to see if chess could be solved mathematically, using equations  
  > **username_2**: The question is solved for arbitrary boards: http://books.google.de/books?id=QxX2CX5OVMsC&pg=PA337&lpg=PA337&dq=knight+metric&source=bl&ots=3J5nDWweOY&sig=_-pQwRWZrh0fI9SHzmkxlCb-Xcc&hl=de&sa=X&ei=-FkoU6WaLen8ywOjgoHoDg&ved=0CDIQ6AEwAA  
  
  ---
  
  ## 4 answers
  
  ### Answer by username_3 on 2014-01-16. Score: 6 | Accepted answer
  
  The furthest distance is from one corner to the opposite one. You can get from a1 to h8 in six moves, for example a1,c2,d4,f3,e5,g6,h8. There are few pairs of squares that take more than four moves.
  
  
  ---
  
  ### Answer by username_4 on 2014-01-13. Score: 3
  
  N can be infinite. I can always make a zillion knight moves. So I expect you really want to know the smallest number of moves a Knight needs to get from square A to square B.
  
  Some N's won't work. A Knight on a1 can't get to b3 in any even number of moves.
  
  One thing we know - if the start and end squares are the same color, it will take an even number of moves. If they are different colors, it will take an odd number of moves.
  
  It doesn't take long to figure out the longest path on the board (a8 to h1 for example) requires six moves. Note the start and end squares are the same color. For alternating colors, the requirement is 5 moves, max.
  
  I don't think there will be an equation where one enters the square locations and a single number comes out.
  
  > **Comments:**
  > **username_5**: I think "he _has_ to move N moves. how big could N be?" means that the question is about the smallest number.  
  > **username_0**: The question is indeed about the smallest number  
  
  ---
  
  ### Answer by username_6 on 2014-09-02. Score: 2
  
  If the knight cannot touch the same square twice then the answer is 63. See [Knight's tour](http://en.wikipedia.org/wiki/Knight%27s_tour)
  
  A coworker of mine wrote the software to determine the route a long time ago.
  
  > **Comments:**
  > **username_0**: may i take a look at the software source code? or is it not open source?  
  > **username_6**: Sadly, it is not.  
  
  ---
  
  ### Answer by username_7 on 2014-01-13. Score: 1
  
  I think the options are finites (not infinite) is possible calculate all the possible moves from f3 to g8 so the Knight can take the Bishop but its a longest number.
  
  Since the chess board is finite in dimensions (8x8) all the possible moves can be calculated, but off course it will be again a very longest number.
  
  
  ---
  
  