Answers.Body: <p>Three moves is probably in the realm where you could manually brute-force it, although it may take some effort. </p>
  
  <p>Pick a move, a reply, a second move, and a second reply. Then start looking at whether White has a checkmate from that position. If not, then White's second move was incorrect, so change it. If you eliminate all possible White second moves this way, then go back to White's first move, and change it. If you eliminate all White first moves too, then you have proven that a mate in 3 does not exist.</p>
  
  <p>If you do find a White checkmate from one of these positions, then change Black's previous move. If the solution is valid, White will have a checkmate for <em>all</em> possible Black replies.</p>
  
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2020-03-21T00:08:56.750Z
Answers.Text: Brute force it? Probably not. Three moves in chess, depending on the number of pieces, can easily run into the millions of possibilities. After just three moves in the opening, there are over 121 million possibilities, and after just four, 319 billion. You might stumble upon the answer as we do when calculating any position as a human, but you will not brute force virtually any position with even a minimum of pieces.
Answers.UserDisplayName: PhishMaster
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2020-03-21T00:38:22.050Z
Answers.Text: There may be 121 million possibilities after 3 moves in the opening, but that's *six* ply, and a mate in 3 problem is only 5 ply, reducing it to under 5 million. You don't have to explore all possibilities, though, and that saves time. Not finding a mate after a particular Black second move means White's second move was incorrect, so you don't have to explore the other possible Black responses to that move. And, of course, if checkmate is imminent, the lines can be quite forcing. Whether it's feasible does depend on the position.
Answers.UserDisplayName: D M
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2020-03-21T00:41:43.917Z
Answers.Text: I did not consider that half ply, but still, even at 1,000,000, or less, you are not going to "brute force it". You can maybe find it the way we calculate everything...by pattern recognition, but not true brute force. There are people, who will take that at face value, when it is mostly impossible.
Answers.UserDisplayName: PhishMaster
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2020-03-21T00:54:41.537Z
Answers.Text: By choosing Black's moves wisely/luckily, you essentially reduce it to 3 ply, since you'd then only need to go through all possible White moves. In some positions that's tedious but doable; in some positions it's admittedly not feasible. But... without using a computer, how *else* are you going to prove an arbitrary position is *not* solvable?
Answers.UserDisplayName: D M
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2020-03-21T01:02:29.350Z
Answers.Text: My problem is with that specific term. It renders part of your answer incorrect. I am not saying it is not solvable, just HOW.
Answers.UserDisplayName: PhishMaster
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2020-03-21T08:45:51.623Z
Answers.Text: Is there some kind of notation or mathematical method I can use? I'd like to learn something from the process
Answers.UserDisplayName: OrigamiEye
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2020-03-21T08:49:21.860Z
Answers.Text: What is ply, as in "that's six ply"?
Answers.UserDisplayName: OrigamiEye
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2020-03-21T12:58:17.930Z
Answers.Text: @OrigamiEye [Ply](https://en.wikipedia.org/wiki/Ply_(game_theory))
Answers.UserDisplayName: Ellie
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2020-03-21T16:00:36.790Z
Answers.Text: @PhishMaster Maybe brute force isn't the correct term, but I'm not exactly sure how else to describe it. Semi-brute-force?
Answers.UserDisplayName: D M
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2020-03-21T16:05:17.090Z
Answers.Text: @DM I understand what you are trying to say, but maybe just qualifying it by saying as much as a human can do reasonably...a systematic search. Still, the best way is still using the specialized engine to know for sure.
Answers.UserDisplayName: PhishMaster
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2020-03-20T23:12:20.333Z
Answers.LastActivityDate: 2020-03-20T23:12:20.333Z
Answers.UserDisplayName: D M
Answers.Body: <p>The only way to prove it with 100% accuracy is to use a special engine. Since you do not want to see the solution yourself, then you could ask someone you trust to use it for you. Having a friend sit there and attempt to solve it will not really prove anything since he is human, and may not be strong enough to guarantee a correct answer.</p>
  
  <p>You are almost asking an impossible question in that you want to know the answer, but not willing to let anyone see it or to use a computer to solve it yourself. You cannot have it all.</p>
  
  <p>There are special engines that are designed to prove or disprove mate-in-x problems. The ChessBase program Fritz has always had this function. I am not sure if others do though.</p>
  
  <p>Here is a screenshot of the help file.</p>
  
  <p><a href="https://i.sstatic.net/WGMKs.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/WGMKs.png" alt="enter image description here"></a></p>
  
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2020-03-21T08:47:27.777Z
Answers.Text: I will look into it, once I confirm it still works I will accept your answer. I am on Mac though.
Answers.UserDisplayName: OrigamiEye
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2020-03-21T10:59:55.547Z
Answers.Text: There may be others, but ChessBase products only run on a PC. They made one attempt a long time ago, and stopped, deeming it not worth it business-wise.
Answers.UserDisplayName: PhishMaster
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2020-03-21T14:09:16.730Z
Answers.Text: @OrigamiEye If you would like, if you have a chess.com account (of you can create one for free), you can send me the problem via a message there, and I can run it through Fritz with the special mate-in-x engine and send you as much or as little information about the results as you would like. I could simply confirm that the mate is there all the way to sending you the answer, now or in the future if you should change your mind later.
Answers.UserDisplayName: PhishMaster
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2020-03-20T21:31:50.777Z
Answers.LastActivityDate: 2020-03-20T21:31:50.777Z
Answers.UserDisplayName: PhishMaster
Body: <p>I have been working on a checkmate-in-3 problem for a long time. So long that I am becoming convinced it is not solvable. </p>
  
  <p>Is there a way to prove it is not solvable?</p>
  
  <p>I want to avoid putting the problem in an engine, in case it will show me a solution. For the same reason I do not want to share the problem.</p>
  
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2020-03-20T21:04:49.103Z
Comments.Text: Why not just give the position to a friend, ask him to test it with an engine, and to tell you whether it's solvable or not?
Comments.UserDisplayName: emdio
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2020-03-20T21:36:59.540Z
Comments.Text: Just to be sure, have you checked en passant as a possible solution? Or sometimes people don't realize that castle is still possible.
Comments.UserDisplayName: Akavall
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2020-03-22T00:03:27.457Z
Comments.Text: I used to have a mate in three that I liked to give people.  No one I showed it to ever solved it.  After that experience I am never convinced that any puzzle is not solvable without using a computer to check it.
Comments.UserDisplayName: Michael West
Tags: <checkmate><problems>
Title: Is there a way to prove a checkmate in 3 problem is not solvable?
ThreadText: # Is there a way to prove a checkmate in 3 problem is not solvable?
  
  (Asked by: username_0 on 2020-03-20)
  
  I have been working on a checkmate-in-3 problem for a long time. So long that I am becoming convinced it is not solvable.
  
  Is there a way to prove it is not solvable?
  
  I want to avoid putting the problem in an engine, in case it will show me a solution. For the same reason I do not want to share the problem.
  
  **Tags:** checkmate, problems
  
  > **Comments:**
  > **username_1**: Why not just give the position to a friend, ask him to test it with an engine, and to tell you whether it's solvable or not?  
  > **username_2**: Just to be sure, have you checked en passant as a possible solution? Or sometimes people don't realize that castle is still possible.  
  > **username_3**: I used to have a mate in three that I liked to give people.  No one I showed it to ever solved it.  After that experience I am never convinced that any puzzle is not solvable without using a computer to check it.  
  
  ---
  
  ## 2 answers
  
  ### Answer by username_4 on 2020-03-20. Score: 4
  
  Three moves is probably in the realm where you could manually brute-force it, although it may take some effort.
  
  Pick a move, a reply, a second move, and a second reply. Then start looking at whether White has a checkmate from that position. If not, then White's second move was incorrect, so change it. If you eliminate all possible White second moves this way, then go back to White's first move, and change it. If you eliminate all White first moves too, then you have proven that a mate in 3 does not exist.
  
  If you do find a White checkmate from one of these positions, then change Black's previous move. If the solution is valid, White will have a checkmate for *all* possible Black replies.
  
  > **Comments:**
  > **username_5**: Brute force it? Probably not. Three moves in chess, depending on the number of pieces, can easily run into the millions of possibilities. After just three moves in the opening, there are over 121 million possibilities, and after just four, 319 billion. You might stumble upon the answer as we do when calculating any position as a human, but you will not brute force virtually any position with even a minimum of pieces.  
  > **username_4**: There may be 121 million possibilities after 3 moves in the opening, but that's *six* ply, and a mate in 3 problem is only 5 ply, reducing it to under 5 million. You don't have to explore all possibilities, though, and that saves time. Not finding a mate after a particular Black second move means White's second move was incorrect, so you don't have to explore the other possible Black responses to that move. And, of course, if checkmate is imminent, the lines can be quite forcing. Whether it's feasible does depend on the position.  
  > **username_5**: I did not consider that half ply, but still, even at 1,000,000, or less, you are not going to "brute force it". You can maybe find it the way we calculate everything...by pattern recognition, but not true brute force. There are people, who will take that at face value, when it is mostly impossible.  
  > **username_4**: By choosing Black's moves wisely/luckily, you essentially reduce it to 3 ply, since you'd then only need to go through all possible White moves. In some positions that's tedious but doable; in some positions it's admittedly not feasible. But... without using a computer, how *else* are you going to prove an arbitrary position is *not* solvable?  
  > **username_5**: My problem is with that specific term. It renders part of your answer incorrect. I am not saying it is not solvable, just HOW.  
  > **username_0**: Is there some kind of notation or mathematical method I can use? I'd like to learn something from the process  
  > **username_0**: What is ply, as in "that's six ply"?  
  > **username_6**: @username_0 [Ply](https://en.wikipedia.org/wiki/Ply_(game_theory))  
  > **username_4**: @username_5 Maybe brute force isn't the correct term, but I'm not exactly sure how else to describe it. Semi-brute-force?  
  > **username_5**: @DM I understand what you are trying to say, but maybe just qualifying it by saying as much as a human can do reasonably...a systematic search. Still, the best way is still using the specialized engine to know for sure.  
  
  ---
  
  ### Answer by username_5 on 2020-03-20. Score: 3
  
  The only way to prove it with 100% accuracy is to use a special engine. Since you do not want to see the solution yourself, then you could ask someone you trust to use it for you. Having a friend sit there and attempt to solve it will not really prove anything since he is human, and may not be strong enough to guarantee a correct answer.
  
  You are almost asking an impossible question in that you want to know the answer, but not willing to let anyone see it or to use a computer to solve it yourself. You cannot have it all.
  
  There are special engines that are designed to prove or disprove mate-in-x problems. The ChessBase program Fritz has always had this function. I am not sure if others do though.
  
  Here is a screenshot of the help file.
  
  [![enter image description here](https://i.sstatic.net/WGMKs.png)](https://i.sstatic.net/WGMKs.png)
  
  > **Comments:**
  > **username_0**: I will look into it, once I confirm it still works I will accept your answer. I am on Mac though.  
  > **username_5**: There may be others, but ChessBase products only run on a PC. They made one attempt a long time ago, and stopped, deeming it not worth it business-wise.  
  > **username_5**: @username_0 If you would like, if you have a chess.com account (of you can create one for free), you can send me the problem via a message there, and I can run it through Fritz with the special mate-in-x engine and send you as much or as little information about the results as you would like. I could simply confirm that the mate is there all the way to sending you the answer, now or in the future if you should change your mind later.  
  
  ---
  
  