Answers.Body: <p>Since it can't be analyzed with an engine, I made it so :-) I hope you agree that this setting keeps the relevant restriction (the wR only moves once):</p>
  <pre><code>[FEN &quot;8/p7/rp6/rp6/pP6/R7/8/K6k w - - 0 1&quot;]
  </code></pre>
  <p>Note that Kb3 is impossible here, so you must be a bit careful with outflanking. But Kb1 is a clear #11. (A problem solving engine could give all shortest variants, but that takes tiiiime...)</p>
  
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2023-07-20T14:39:11.700Z
Answers.Text: I guess 11 turns is correct
Answers.UserDisplayName: Oliver
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2023-07-20T15:45:36.540Z
Answers.Text: Clever idea Hauke
Answers.UserDisplayName: Laska
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2023-07-20T23:36:50.480Z
Answers.Text: I don't get it, why's this enforce the criterion? What awful thing happens if the rook moves before a mate is available? Black moves a pawn, but that alone does nothing if white rook moving can accelerate mate.
Answers.UserDisplayName: OverLordGoldDragon
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2023-07-21T17:09:46.183Z
Answers.Text: A good question OverLordGoldDragon. If there’s no other material on the board then wKR can never force checkmate bK if Black has the right to pass. So giving Black extra units achieves this effect, once any of them is unblocked
Answers.UserDisplayName: Laska
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Answers.CreationDate: 2023-07-21T20:17:36.823Z
Answers.Text: @OverLordGoldDragon: At least one black rook comes out of the pawn prison if White allows a3, with an obvious non-win. Thus the rook may only move to mate.
Answers.UserDisplayName: Hauke Reddmann
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Answers.CreationDate: 2023-07-21T20:21:59.163Z
Answers.Text: @Laska @ Hauke this requires at least 3 moves by black, 4 to do anything other than break out. So again I don't see how this setup doesn't permit wR to move twice or more.
Answers.UserDisplayName: OverLordGoldDragon
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2023-07-22T13:31:35.153Z
Answers.Text: @OverLordGoldDragon: Correct, but you can't even mate with K+R vs K+infinite pass moves. The wR *can* move more than once, but you want to reach a goal (mate), and *doing* a move is utterly useless.
Answers.UserDisplayName: Hauke Reddmann
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2023-07-22T22:52:13.143Z
Answers.Text: I figured moving the rook could possibly accelerate mate, I guess you're saying that's not so here. Interestingly, I fed this to [Lichess Stockfish 14](https://lichess.org/analysis/standard/8/p7/rp6/rp6/pP6/R7/8/K6k_w_-_-_0_1), and it fails with its initial Depth 67 - I put it up to Depth 99, but I gave up waiting on Depth 77. It keeps thinking Ka2. Yet, the moment I play Kb1, it instantly realizes mate in 11 for white. I [asked](https://chess.stackexchange.com/q/42605/33019) about it.
Answers.UserDisplayName: OverLordGoldDragon
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2023-07-23T13:51:50.307Z
Answers.Text: wR can move any number of times it doesn’t help. The point is that if Black can pass whenever he wants then there’s no way for KR to mate K. So the single rook move must be checkmating
Answers.UserDisplayName: Laska
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Answers.CreationDate: 2023-07-20T09:36:57.633Z
Answers.LastActivityDate: 2023-07-20T09:36:57.633Z
Answers.UserDisplayName: Hauke Reddmann
Answers.Body: <p><strong>Answer is edited.</strong> Initial conclusion was that it's impossible.</p>
  <p>First of all, the only rook's move must be the last move (you cannot check by a king), so it's all about kings dancing. White are willing to checkmate here either when the black king is on <code>a</code> column opposed by the white king on <code>c</code> column or when the black king is cornered at <code>a8</code> with the white king on <code>a6/b6/c7</code>. First option is typically avoidable by black so white's strategy is to gradually force the black king into the corner by using opposition.</p>
  <p>Position that forces a king to step back is when it's opposed by the other king and the distance is exactly one row. For the king whose turn is next it's <em>bad opposition</em>, for the king just moved it's <em>good opposition</em>. In this play whenever black happen to obtain good opposition they can maintain it by mirroring the white king's moves (rook will not interfere here as it will always be blocked by the king). This way black keep <em>odd</em> number of rows between the kings. It works vice versa - whenever black ends a turn opposing  the white king with <em>odd</em> number of rows between them - they are safe. So, <em>good</em> and <em>bad</em> oppositions should be extended from single row to any <em>odd</em> number of rows. Initially white can immediately obtain good opposition by <code>1. Ka2</code> but the catch here is that <strong>white need to approach the black king and black do not have to</strong>.</p>
  <p>So the detailed strategy for white should be this:</p>
  <ol>
  <li>Always avoid black's <em>good opposition</em></li>
  <li>Do not let black king to the rook</li>
  <li>Approach the black king</li>
  <li>Use threat of opposing the black king on <code>a</code> column from <code>c</code></li>
  </ol>
  <p>Strategy for black should be this:</p>
  <ol>
  <li>Obtain <em>good opposition</em> whenever possible</li>
  <li>Threaten to get to the rook (when white king is to the right of <code>c</code> column)</li>
  <li>Preferrably maintain odd number of rows to the black king</li>
  <li>Keep distance from the white king</li>
  </ol>
  <pre><code>[FEN &quot;k7/8/8/8/8/8/8/K1R5 w - - 0 1&quot;]
  
  1. Ka2 {b1 or b2 allow good opposition for black} Kb8
      (1. Kb1 Kb7!)
      (1. Kb2 Kb8!)
      (1... Ka7 {allows good opposition for white} 2. Ka3)
      (1... Kb7 {allows good opposition for white} 2. Kb3)
  2. Kb2 Ka8
      (2. Ka1 {same for 2. Ka3, allows good opposition for black} Ka7! {black are safe})
      (2. Kb1 {same for 2. Kb3, allows good opposition for black} Kb7! {black are safe})
      (2... Ka7 3. Ka3)
      (2... Kb7 3. Kb3)
  3. Kc3 Kb7
      (3. Ka2 Kb8 {Repeats the first turn})
      (3. Kc2 Kb8. 4. Kc3 Kc7! {black are safe}
          (4. Kb2 Ka8 {Repeats the second turn})
          (4. Kd2 {Or any other to d column} Kb7 {black king gets space and approaches the rook})
          (4. Kb1 {same for 4. Kb3} Kb7!)
      )
      (3... Ka7 Kc4 {white is just getting closer})
      (3... Kb8 4. Kb4)
  4. Kb3 {The white king is opposing similar to 1 ...Kb8 2. Kb2 but it's two rows closer. Now white can repeat this 2-move pattern to approach the black king} Ka7 (same reason as for 2... Ka8)
  5. Kc4 Kb6
  6. Kb4 Ka6
  7. Kc5 {Now he threat Ra1# is active} Kb7
      (7... Ka5 8. Ra1#)
      (7... Ka7 8. Kc6 {repeating 7. Kc5 but one row closer to the edge})
  8. Kb5 {same as 6. Kb4 but closer to the edge} Ka7
  9. Kc6 Kb8
  10. Kb6 Ka8
  11. Rc8#
  </code></pre>
  <p>And remarkably, it matches the 11 turns produced by engine for edited position. For me, it's not &quot;simple one&quot; ©.</p>
  
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2023-07-20T03:07:08.217Z
Answers.Text: By the way, how can I make this cool playable chess diagram into the answer?
Answers.UserDisplayName: Oliver
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2023-07-20T05:10:19.417Z
Answers.Text: it is described [here](https://chess.meta.stackexchange.com/questions/179/how-do-i-add-a-replayer-to-my-post)
Answers.UserDisplayName: Piro
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2023-07-20T14:23:18.423Z
Answers.Text: I still couldn't make the player work :( probably I'm missing something. I would appreciate a proper edit to the answer that helps with formatting player's code.
Answers.UserDisplayName: Oliver
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2023-07-20T14:49:30.043Z
Answers.Text: I expected a solution to have a lot of options for black and the resulting single best option for white, to show check mate no matter what black does ?
Answers.UserDisplayName: Falco
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2023-07-20T14:53:26.280Z
Answers.Text: @Falco due to nature of this particular case it's white who are at risk to make a mistake and miss a win. Any time black obtain the good opposition the win is gone. So, displaying options for winning side is quite unusual but appropriate for this puzzle.
Answers.UserDisplayName: Oliver
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2023-07-20T15:05:08.127Z
Answers.Text: I edited your diagram. You had to place quotes around the FEN. ;-)
Answers.UserDisplayName: IT M
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2023-07-20T03:06:21.523Z
Answers.LastActivityDate: 2023-07-20T15:32:32.753Z
Answers.LastEditDate: 2023-07-20T15:32:32.753Z
Answers.UserDisplayName: Oliver
Answers.Body: <p>This is a simple one.
  You can't make progress once the K's are opposed and thus the only solution is outflanking.</p>
  <pre><code>[FEN &quot;k7/8/8/8/8/8/8/K1R5 w - - 0 1&quot;]
  
  1. Ka2 Ka7 {is the human approach} (1... Kb8 {forces thinking about opposition} 2.Kb2 {maintaining opposition} Ka8 {since moving up sustains the white opposition, but makes it shorter} (2... Ka7 3.Ka3 {opposition but shorter}) (2... Kb7 3.Kb3 {opposition but shorter}) 3.Kc3 {outflanking = not losing opposition} Kb8 (3...Ka7 4.Kc4 {more of the same, doesn't shorten Blacks imminent death}) (3...Kb7 4.Kb3 {opposition again}) 4.Kb4 {and the opposition story goes on...}) 2. Ka3 Ka6 3. Ka4 Kb6 4. Kb4 Ka6 5. Kc5 {Ka5 won't lead to a solution.} Kb7 6. Kb5 Ka7 7. Kc6 Ka8 8. Kc7 (8. Kb6 {is a bit slower and as GM Ben Finegold would thus say: &quot;wrong!&quot;} Kb8 9. Ka6 Ka8 10. Rc8#) 8... Ka7 9. Ra1#
  </code></pre>
  <p>EDIT: added some more sidelines on request. IMO 4 deep for a sideline is more than sufficient to keep it readable.</p>
  
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2023-07-20T06:47:02.757Z
Answers.Text: @Laska the concept is called "King opposition". Many endgame books teach this topic. Would be sort of difficult to explain it in its entirety in comments section though.
Answers.UserDisplayName: Emre Bener
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2023-07-19T11:58:50.923Z
Answers.LastActivityDate: 2023-07-20T15:02:16.070Z
Answers.LastEditDate: 2023-07-20T15:02:16.070Z
Answers.UserDisplayName: IT M
Body: <pre><code>[Title &quot;White to play and win - only moving the rook once&quot;]
  [fen &quot;k7/8/8/8/8/8/8/K1R5 w - - 0 1&quot;]
  </code></pre>
  <p>This is an exercise in using the opposition and outflanking from John Hawkins' Amateur to IM. Obviously your engine isn't going to help.</p>
  
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2023-07-20T12:17:05.627Z
Comments.Text: I don't know Hakins' works but I have seen this excellent exercice associated to Dvoretsky. I wonder who invented it first.
Comments.UserDisplayName: Evargalo
Tags: <endgame><puzzles><rook-endgame>
Title: White to play and win - only moving the rook once
ThreadText: # White to play and win - only moving the rook once
  
  (Asked by: username_0 on 2023-07-19)
  
  ```
  [Title "White to play and win - only moving the rook once"]
  [fen "k7/8/8/8/8/8/8/K1R5 w - - 0 1"]
  
  ```
  
  This is an exercise in using the opposition and outflanking from John Hawkins' Amateur to IM. Obviously your engine isn't going to help.
  
  **Tags:** endgame, puzzles, rook-endgame
  
  > **Comments:**
  > **username_1**: I don't know Hakins' works but I have seen this excellent exercice associated to Dvoretsky. I wonder who invented it first.  
  
  ---
  
  ## 3 answers
  
  ### Answer by username_8 on 2023-07-19. Score: 13 | Accepted answer
  
  This is a simple one.
  You can't make progress once the K's are opposed and thus the only solution is outflanking.
  
  ```
  [FEN "k7/8/8/8/8/8/8/K1R5 w - - 0 1"]
  
  1. Ka2 Ka7 {is the human approach} (1... Kb8 {forces thinking about opposition} 2.Kb2 {maintaining opposition} Ka8 {since moving up sustains the white opposition, but makes it shorter} (2... Ka7 3.Ka3 {opposition but shorter}) (2... Kb7 3.Kb3 {opposition but shorter}) 3.Kc3 {outflanking = not losing opposition} Kb8 (3...Ka7 4.Kc4 {more of the same, doesn't shorten Blacks imminent death}) (3...Kb7 4.Kb3 {opposition again}) 4.Kb4 {and the opposition story goes on...}) 2. Ka3 Ka6 3. Ka4 Kb6 4. Kb4 Ka6 5. Kc5 {Ka5 won't lead to a solution.} Kb7 6. Kb5 Ka7 7. Kc6 Ka8 8. Kc7 (8. Kb6 {is a bit slower and as GM Ben Finegold would thus say: "wrong!"} Kb8 9. Ka6 Ka8 10. Rc8#) 8... Ka7 9. Ra1#
  
  ```
  
  EDIT: added some more sidelines on request. IMO 4 deep for a sideline is more than sufficient to keep it readable.
  
  > **Comments:**
  > **username_9**: @username_4 the concept is called "King opposition". Many endgame books teach this topic. Would be sort of difficult to explain it in its entirety in comments section though.  
  
  ---
  
  ### Answer by username_2 on 2023-07-20. Score: 8
  
  Since it can't be analyzed with an engine, I made it so :-) I hope you agree that this setting keeps the relevant restriction (the wR only moves once):
  
  ```
  [FEN "8/p7/rp6/rp6/pP6/R7/8/K6k w - - 0 1"]
  
  ```
  
  Note that Kb3 is impossible here, so you must be a bit careful with outflanking. But Kb1 is a clear #11. (A problem solving engine could give all shortest variants, but that takes tiiiime...)
  
  > **Comments:**
  > **username_3**: I guess 11 turns is correct  
  > **username_4**: Clever idea username_2  
  > **username_5**: I don't get it, why's this enforce the criterion? What awful thing happens if the rook moves before a mate is available? Black moves a pawn, but that alone does nothing if white rook moving can accelerate mate.  
  > **username_4**: A good question username_5. If there’s no other material on the board then wKR can never force checkmate bK if Black has the right to pass. So giving Black extra units achieves this effect, once any of them is unblocked  
  > **username_2**: @username_5: At least one black rook comes out of the pawn prison if White allows a3, with an obvious non-win. Thus the rook may only move to mate.  
  > **username_5**: @username_4 @ username_2 this requires at least 3 moves by black, 4 to do anything other than break out. So again I don't see how this setup doesn't permit wR to move twice or more.  
  > **username_2**: @username_5: Correct, but you can't even mate with K+R vs K+infinite pass moves. The wR *can* move more than once, but you want to reach a goal (mate), and *doing* a move is utterly useless.  
  > **username_5**: I figured moving the rook could possibly accelerate mate, I guess you're saying that's not so here. Interestingly, I fed this to [Lichess Stockfish 14](https://lichess.org/analysis/standard/8/p7/rp6/rp6/pP6/R7/8/K6k_w_-_-_0_1), and it fails with its initial Depth 67 - I put it up to Depth 99, but I gave up waiting on Depth 77. It keeps thinking Ka2. Yet, the moment I play Kb1, it instantly realizes mate in 11 for white. I [asked](https://chess.stackexchange.com/q/42605/33019) about it.  
  > **username_4**: wR can move any number of times it doesn’t help. The point is that if Black can pass whenever he wants then there’s no way for KR to mate K. So the single rook move must be checkmating  
  
  ---
  
  ### Answer by username_3 on 2023-07-20. Score: 3
  
  **Answer is edited.** Initial conclusion was that it's impossible.
  
  First of all, the only rook's move must be the last move (you cannot check by a king), so it's all about kings dancing. White are willing to checkmate here either when the black king is on `a` column opposed by the white king on `c` column or when the black king is cornered at `a8` with the white king on `a6/b6/c7`. First option is typically avoidable by black so white's strategy is to gradually force the black king into the corner by using opposition.
  
  Position that forces a king to step back is when it's opposed by the other king and the distance is exactly one row. For the king whose turn is next it's *bad opposition*, for the king just moved it's *good opposition*. In this play whenever black happen to obtain good opposition they can maintain it by mirroring the white king's moves (rook will not interfere here as it will always be blocked by the king). This way black keep *odd* number of rows between the kings. It works vice versa - whenever black ends a turn opposing the white king with *odd* number of rows between them - they are safe. So, *good* and *bad* oppositions should be extended from single row to any *odd* number of rows. Initially white can immediately obtain good opposition by `1. Ka2` but the catch here is that **white need to approach the black king and black do not have to**.
  
  So the detailed strategy for white should be this:
  
  1. Always avoid black's *good opposition*
  2. Do not let black king to the rook
  3. Approach the black king
  4. Use threat of opposing the black king on `a` column from `c`
  
  Strategy for black should be this:
  
  1. Obtain *good opposition* whenever possible
  2. Threaten to get to the rook (when white king is to the right of `c` column)
  3. Preferrably maintain odd number of rows to the black king
  4. Keep distance from the white king
  
  ```
  [FEN "k7/8/8/8/8/8/8/K1R5 w - - 0 1"]
  
  1. Ka2 {b1 or b2 allow good opposition for black} Kb8
      (1. Kb1 Kb7!)
      (1. Kb2 Kb8!)
      (1... Ka7 {allows good opposition for white} 2. Ka3)
      (1... Kb7 {allows good opposition for white} 2. Kb3)
  2. Kb2 Ka8
      (2. Ka1 {same for 2. Ka3, allows good opposition for black} Ka7! {black are safe})
      (2. Kb1 {same for 2. Kb3, allows good opposition for black} Kb7! {black are safe})
      (2... Ka7 3. Ka3)
      (2... Kb7 3. Kb3)
  3. Kc3 Kb7
      (3. Ka2 Kb8 {Repeats the first turn})
      (3. Kc2 Kb8. 4. Kc3 Kc7! {black are safe}
          (4. Kb2 Ka8 {Repeats the second turn})
          (4. Kd2 {Or any other to d column} Kb7 {black king gets space and approaches the rook})
          (4. Kb1 {same for 4. Kb3} Kb7!)
      )
      (3... Ka7 Kc4 {white is just getting closer})
      (3... Kb8 4. Kb4)
  4. Kb3 {The white king is opposing similar to 1 ...Kb8 2. Kb2 but it's two rows closer. Now white can repeat this 2-move pattern to approach the black king} Ka7 (same reason as for 2... Ka8)
  5. Kc4 Kb6
  6. Kb4 Ka6
  7. Kc5 {Now he threat Ra1# is active} Kb7
      (7... Ka5 8. Ra1#)
      (7... Ka7 8. Kc6 {repeating 7. Kc5 but one row closer to the edge})
  8. Kb5 {same as 6. Kb4 but closer to the edge} Ka7
  9. Kc6 Kb8
  10. Kb6 Ka8
  11. Rc8#
  
  ```
  
  And remarkably, it matches the 11 turns produced by engine for edited position. For me, it's not "simple one" ©.
  
  > **Comments:**
  > **username_3**: By the way, how can I make this cool playable chess diagram into the answer?  
  > **username_6**: it is described [here](https://chess.meta.stackexchange.com/questions/179/how-do-i-add-a-replayer-to-my-post)  
  > **username_3**: I still couldn't make the player work :( probably I'm missing something. I would appreciate a proper edit to the answer that helps with formatting player's code.  
  > **username_7**: I expected a solution to have a lot of options for black and the resulting single best option for white, to show check mate no matter what black does ?  
  > **username_3**: @username_7 due to nature of this particular case it's white who are at risk to make a mistake and miss a win. Any time black obtain the good opposition the win is gone. So, displaying options for winning side is quite unusual but appropriate for this puzzle.  
  > **username_8**: I edited your diagram. You had to place quotes around the FEN. ;-)  
  
  ---
  
  