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A knight is placed on an infinitely large chess board with no edges. It can only visit each square once. What is the smallest number of moves it can make that would cause it to become trapped?

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what? why there can be minimum? even on 3x3 chess board. – klm123 Jan 17 at 21:12
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It's hard to tell what you're asking. Minimum number of moves to accomplish what? – Mike Earnest Jan 17 at 21:13
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one of the critical requirement is not to visit the same square again, so by using this you are supposed to find the minimum number of moves can a knight can achieve (where the knight cannot move again to another square since it visited there before). – Oray Jan 17 at 21:29
    
@Oray I've edited your question. Is this what you meant? – Deusovi Jan 17 at 21:33
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@jhabbott: The knight doesn't need to have the goal of trapping itself. It might just be inept or confused and do it by mistake. I think the word "smallest" makes the question clear. Perhaps changing "before getting" to "that would cause it to become" would make it more clear that its moves are not subject to some implicit unstated policy (like fleeing to the north), and would avoid problems with infinite move sequences, which have no well defined length, and so (depending on the formalization) could be thought of as inserting undefined elements into the set whose minimum is requested. – Matt Jan 18 at 10:41
up vote 36 down vote accepted

I can get the knight trapped in

15 moves: $$\begin{array} {ccccccccc} \cdot & \cdot & \cdot & \cdot & 5 & \cdot & \cdot & \cdot & \cdot\\ \cdot & 3 & \cdot & \cdot & \cdot & \cdot & \cdot & 7 & \cdot\\ \cdot & \cdot & \cdot & 4 & \cdot & 6 & \cdot & \cdot & \cdot\\ \cdot & \cdot & 2 &\cdot & \cdot & \cdot & 8 & \cdot & \cdot\\ 1 & \cdot & \cdot & \cdot & 15 & \cdot & \cdot & \cdot & 9\\ \cdot & \cdot & S &\cdot & \cdot & \cdot & 10 & \cdot & \cdot\\ \cdot & \cdot & \cdot & 14 & \cdot & 12 & \cdot & \cdot & \cdot\\ \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & 11 & \cdot\\ \cdot & \cdot & \cdot & \cdot & 13 & \cdot & \cdot & \cdot & \cdot\\ \end{array}$$

Just keep going around to block off squares before going into the center.

It's not possible to do it in less because:

If you want to trap the knight, you need to eliminate all eight of its squares that it can escape to. It is not possible to get from one directly to another, so you need to visit an extra square in between each outside square. So that's 8 squares to block off, plus 7 moves in between: 15 moves total.

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Yes, this is the correct answer. Thanks for editing the question by the way :) it was more much clear now. – Oray Jan 17 at 21:35
    
@Oray Glad I could help, and welcome to Puzzling.SE! Hope to see you around more c: – Deusovi Jan 17 at 21:38
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@Oray: That's great! Make sure they haven't been posted before, though - there are a lot of puzzles here. A lot of new people accidentally repost puzzles, and then the puzzles get closed. We don't want you to be discouraged from coming here! – Deusovi Jan 17 at 21:40
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This solution is 15 moves, not 16 – BlueRaja - Danny Pflughoeft Jan 18 at 2:34
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Agree it's only 15 moves... edited the heading and the board to reflect the update, (edit currently pending). @Oray you should accept this answer if it's the correct/best solution. – jhabbott Jan 18 at 6:44

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