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 Post subject: Chess Problem with a twist (Edit: now with the solution!)Posted: Tue Nov 23, 2010 9:35 pm

Joined: Mon Oct 02, 2006 9:38 pm
Location: Brazil
Here is a chess problem that I created (with a friend of mine) some years ago.

It is a "Check-Mate in 2" problem. That is: its the White Player's turn, and you must find a way (and prove it) to check-mate in just 2 moves with no chance for the Black Player to defend.

There is a cool twist in this problem...

Please, if you find the solution do not post it directly here, so others can find it for themselves. Send me a PM instead.
Questions (if they don't lead to the solution) are welcome.

Edit: Also, try to give it a shot only when you are sure of your solution and there is no escape for the Blacks, and you are able to demonstrate the proof.
Otherwise it becomes guessing trial and error... its not so enjoyable this way.
Also too many PMs for me to respond.

Edit: OK, I will give some hints.

HINT 1:
Don't waste your time trying to put this in ChessMaster or DeepBlue. Computer chess programs can't solve this puzzle!

HINT 2: (select the text below to read)
The moves for the check-mate are somehow obvious. Proving that there is no valid escape is the hard part.

Hope you enjoy!

Attachment:

King of Mate.JPG [ 37.5 KiB | Viewed 4080 times ]

SOLUTION:
I have described the complete solution to my best. Excuse-me and please let me know if you find any mistake. English is not my native language.
(select the text below to read)

The solution is: 1. Pxb7,... 2. P=Q++
(White Pawn at a6 takes Black Pawn at b7. After any move from Black, the same Pawn promotes to a Queen and check-mate)

Pretty simple!

BUT, we have to rule out all possible escapes for Black.
It is relatively easy to show that there are no "normal" moves that could defend Black from this check-mate.

But what about Castling?
If Black can still Castle ( 1. ..., O-O), it would be a valid escape, and in that case there would be NO possible mate in 2.

Some of you have not even thought about Castling as an escape, and some have assumed it was a valid escape and failed to see the check-mate.

But, fortunately, Blacks CANNOT Castle anymore, and there is enough evidence of this on the board!
Yes! We are able to INFER some of the PAST moves of this game (Retrograde analysis) and find the proof, so that Blacks cannot Castle and the solution is valid!

That is the hard part, and the real fun of this puzzle.

This proof is mathematically correct, and is not based on mere assumptions or uncertain moves. It is a little extensive, I'm sorry.

Please remember that this is a chess problem (and a Retrograde one). The board position MUST be from a VALID game, but it does not have to be reasonable or expectable in any particular way. It has only to be theoretically possible, no matter how likely it would have happened in a real game.
And it is valid. I have checked it many times.

Lets remember the rules about Castling:

There are a number of cases when castling is not permitted.
(a) Your King has been moved earlier in the game.
(b) The Rook that castles has been moved earlier in the game.
(c) There are pieces standing between your King and Rook.
(d) The King is in check.
(e) The King moves through or ends at a square that is attacked by a piece of the opponent.

It is easy to show that (c), (d) and (e) are not the case here.
So we would have to find proof for (a) or (b).

In this case, we can prove (a). The Black King HAS MOVED earlier in this game, and then returned to its home square where it is now.

Lets see:

(1) Look at the White Bishop (of black-squares). It is still on the board, but it could never had left its initial position (c1), since this position is still blocked by 2 White Pawns (at b2 and d2)

(2) Therefore, it must have been captured on its home square. Later on, a White Pawn has been promoted to that Bishop.

(3) This promotion must have happened on a black square (b8, d8, f8 or h8), since the Bishop is at a black-square.

(4) But squares f8 and h8 are still blocked by the Black Pawns at e7 and g7, and the just-promoted Bishop would have no movement.

(5) Therefore the promotion must have happened at either b8 or d8. There are only 3 possible paths:
(5.1) The promoting White Pawn came from c7 and has captured a Black piece at b8 or
(5.2) The promoting White Pawn came from c7 and has captured a Black piece at d8 or
(5.3) The promoting White Pawn came from d7 and then moved straight to d8

(6) Lets now find how many Black pieces were captured. Counting the remaining pieces we find that 6 (six) Black pieces are out of the game.

(7) But look at the Black Bishop (of black-squares). It is missing! Since its home square (f8) is blocked by the Pawns at e7 and g7, this Bishop must have been captured in its initial position. (by the White Knight, for example)

(8) This capture could NOT have been made by a Pawn. Therefore, we have a maximum of 5 captures made by White Pawns. This conclusion is important!

(9) Now lets look at the White Pawn structure and try to determine how many captures are required to take one Pawn to c7. The pawn at a6 can be either the one born at c2 or the one born at e2:
(9.1) If it is the one from c2, it has made 2 captures to reach a6, and it would take 3 more captures to take another Pawn to c7, either coming from e2 or f2. Therefore having a Pawn at c7 would require all 5 captures available.
(9.2) If it is the one from e2, it has made 4 captures to reach a6, and it would take 1 more capture to take the Pawn born at f2 to e3, totaling 5 captures. The only Pawn that could reach c7 in this scenario is the one coming straight from its home square at c2. Again, having a Pawn at c7 would require all 5 captures available.

10) This invalidates (5.1) and (5.2), since 1 additional capture (in a total of 6) would be required to take the Pawn from c7 to b8 or d8, and this is not possible.

11) Therefore, the only possible path to promotion would be (5.3), but we must prove that it would be possible to have one White Pawn at d7 within the available 5 captures that were made by White Pawns. There are only 2 possible ways:
(11.1) The Pawn at a6 came from c2 with 2 captures, the Pawn at e3 came from f2 with 1 capture, and the Pawn born at e2 reached column d with 1 capture, in a total of 4 captures. This IS POSSIBLE!
(11.2) The Pawn at a6 came from c2 with 2 captures, the Pawn at e3 came from e2 with NO captures, and the Pawn born at f2 reached column d with 2 captures, in a total of 4 captures. This IS ALSO POSSIBLE!

12) Summing it all, we can say for sure that one White Pawn was promoted to a Bishop at square d8, and it reached that square coming straight from column d.

13) Therefore, this Pawn MUST have passed through d7, putting the Black King in check, which had to MOVE to escape.

14) Blacks CANNOT Castle anymore, since the King has already been moved.

And that proves the solution.

That is why you cannot put this problem in ChessMaster and similar chess programs. When you try to set up the position, the game will ASK YOU whether Castling should still be allowed for Blacks. Chess games are not designed to perform this kind of analysis. You would have to write a very specific program to do it. That would not be so easy and would take ages to run on a mid-game position like this one.

Hope you enjoyed!

Regards,
Paulo Peccin

Last edited by ppeccin on Tue Nov 30, 2010 9:32 pm, edited 11 times in total.

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 Post subject: Re: Chess Problem with a twistPosted: Tue Nov 23, 2010 10:49 pm

Joined: Mon Jan 26, 2009 9:00 pm
Edit:

Found the solution. Just read, "Please don't post here."

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 Post subject: Re: Chess Problem with a twistPosted: Tue Nov 23, 2010 10:55 pm

Joined: Sat Mar 24, 2007 6:58 pm
Location: Louisiana, US
PM sent. Edit, Emarx beat me to it while I was composing the message.

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 Post subject: Re: Chess Problem with a twistPosted: Wed Nov 24, 2010 9:13 am

Joined: Mon Oct 02, 2006 9:38 pm
Location: Brazil
No....
I must say that no one has found the solution yet. Check your PMs.

Some people are in a good thinking path, others have just guessed wrong answers.

You must think as if you only had one shot to answer.
Don't send a guess if you are not sure you can prove it.
If not, it becomes a game of trial and error, and its not so enjoyable that way.

Paulo

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 Post subject: Re: Chess Problem with a twistPosted: Wed Nov 24, 2010 9:30 am

Joined: Thu Dec 02, 2004 12:09 pm
Location: Missouri
ppeccin wrote:
Questions (if they don't lead to the solution) are welcome.

I have a question but I'm not sure if it will lead to a solution. I guess I should send a PM.

Carl

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 Post subject: Re: Chess Problem with a twistPosted: Wed Nov 24, 2010 10:14 am

Joined: Wed Jan 28, 2009 7:55 pm
Location: Montana
It's rather simple if Red doesn't get a turn. But assuming that's not the solution, so I'm stumped.

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 Post subject: Re: Chess Problem with a twistPosted: Wed Nov 24, 2010 11:16 am

Joined: Mon Oct 02, 2006 9:38 pm
Location: Brazil
Rentlix wrote:
It's rather simple if Red doesn't get a turn. But assuming that's not the solution, so I'm stumped.

Yes, Red (Black) gets a turn after the first Whites move of course.

Regards,
Paulo

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 Post subject: Re: Chess Problem with a twistPosted: Wed Nov 24, 2010 11:37 am

Joined: Mon Oct 02, 2006 9:38 pm
Location: Brazil
bhearn has found the answer. (he is the first and only one so far)
Congratulations!

bhearn, tell us how you liked the problem (or didn't )
(of course, please don't give any hints for the others still interested)

Keep trying!
Paulo

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 Post subject: Re: Chess Problem with a twistPosted: Wed Nov 24, 2010 12:29 pm

Joined: Mon Jan 26, 2009 9:00 pm
Edit:

Whoops

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 Post subject: Re: Chess Problem with a twistPosted: Wed Nov 24, 2010 12:36 pm

Joined: Thu Sep 24, 2009 12:21 pm
Location: Chichester, England
It's unlikely, but I think I may have it. Read the white. Also, it's in Pig Latin :

Ishopbay romfay B4ay otay E7ay.
Ueenqay romfay G4ay otay B4ay.

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 Post subject: Re: Chess Problem with a twistPosted: Wed Nov 24, 2010 1:09 pm

Joined: Tue Aug 11, 2009 2:44 pm
ppeccin wrote:
bhearn, tell us how you liked the problem (or didn't )
(of course, please don't give any hints for the others still interested)

I liked it very much, with one slight reservation, which I can't mention here without giving something away. I will say that this is not your typical "mate in 2" problem; it's much more interesting than that.

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 Post subject: Re: Chess Problem with a twistPosted: Wed Nov 24, 2010 2:12 pm

Joined: Mon Oct 02, 2006 9:38 pm
Location: Brazil
SEBUVER wrote:
It's unlikely, but I think I may have it. Read the white. Also, it's in Pig Latin :

No, its not that either... Sorry.

Please, don't put answers here. Send me a PM.
Also, try to give it a shot only when you are sure of your solution.
Otherwise it becomes guessing.

If you'd like, I can give you a small hint. Ask me via PM.

Don't give up!
Paulo

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 Post subject: Re: Chess Problem with a twistPosted: Wed Nov 24, 2010 2:15 pm

Joined: Sat Jul 11, 2009 1:09 pm
Location: My House
I've sent a pm. I'm terrible at chess but I think that I may have got the solution!

Alex

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 Post subject: Re: Chess Problem with a twistPosted: Wed Nov 24, 2010 2:29 pm

Joined: Thu Dec 02, 2004 12:09 pm
Location: Missouri
PM sent. I'm 99.9% sure I have white's last 2 moves correct. One part of the proof though I'm not certain of.

Carl

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 Post subject: Re: Chess Problem with a twistPosted: Wed Nov 24, 2010 2:56 pm

Joined: Fri May 15, 2009 3:12 pm
I've got solution, I'm sure.

edit : finaly not 100% sure. But more than 0%.

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 Post subject: Re: Chess Problem with a twistPosted: Wed Nov 24, 2010 3:14 pm

Joined: Mon Oct 02, 2006 9:38 pm
Location: Brazil
Wow, I'm overwhelmed by the amount of PM's..... Sorry if I can't answer all of them so quickly.

But I must say that, as of now, still only bhearn has found the solution.

Sorry WilliamF, but you can't be sure (of what you sent me via PM).

Again, there are some people in the right direction!

Regards,
Paulo

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 Post subject: Re: Chess Problem with a twistPosted: Wed Nov 24, 2010 6:07 pm

Joined: Wed Jan 28, 2009 7:55 pm
Location: Montana
SEBUVER wrote:
It's unlikely, but I think I may have it.

No, the king could just take the bishop or the pawn could take the queen.

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 Post subject: Re: Chess Problem with a twistPosted: Wed Nov 24, 2010 6:55 pm

Joined: Mon Oct 02, 2006 9:38 pm
Location: Brazil
Please guys, don't give or discuss solutions here.

Just questions that don't spoil the solution are allowed.

I have edited the original post to include hints. Read them only if you need!

Thanks,
Paulo

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 Post subject: Re: Chess Problem with a twistPosted: Wed Nov 24, 2010 9:37 pm

Joined: Thu Dec 02, 2004 12:09 pm
Location: Missouri
PM sent to bhearn and ppeccin... I think I've got it now.

bhearn wrote:
I liked it very much, with one slight reservation...

Curious what your reservation is... if the solution that I PM'ed you is correct please PM me to let me know. Over all great puzzle and you are certainly correct... finding the mate it 2 is easy... proving the mate in two... very interesting.

Assuming I'm correct...
Carl

P.S. And just spotted the hidden hint above so I hid part of my comment too as I came to the same conclusion.

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 Post subject: Re: Chess Problem with a twist (Edit: now with 2 hints!)Posted: Thu Nov 25, 2010 2:08 am

Joined: Sat Mar 24, 2007 6:58 pm
Location: Louisiana, US
I recieved a PM that my super obvious (to me) solution could be blocked by a move by one of Red's peices. That would maybe bump my checkmate up to three moves tops. Unless there is some type of invalid parameter on this chessboard, I don't see why a chess simulator wouldn't be able to solve it. Time to fire up my old early 90's era Radio Shack brand electronic chess board (it's been collecting dust in my closet since the late 90s.

Unrelated, there is also another classic mate problem I am aware of, called "Fool's Mate", which gets white checkmated after two moves, no pieces captured

<new game>
w1: Pawn to F3
b1: Pawn to E5
w2: Pawn to G4
b2: Queen to H4 <checkmate>

I sometimes entertain myself by setting up the chess sets at the local coffee shops to this position!

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 Post subject: Re: Chess Problem with a twist (Edit: now with 2 hints!)Posted: Thu Nov 25, 2010 9:14 am

Joined: Mon Oct 02, 2006 9:38 pm
Location: Brazil
Congratulations wwwmwww!
You're the second one to find the answer.

Please tell us what you think, and whether you agree that a computer will have trouble solving this puzzle!
(please be careful not to give any hints)

Regards,
Paulo

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 Post subject: Re: Chess Problem with a twist (Edit: now with 2 hints!)Posted: Thu Nov 25, 2010 10:28 am

Joined: Wed May 13, 2009 4:58 pm
Location: Vancouver, Washington
ppeccin wrote:
HINT 1: Don't waste your time trying to put this in ChessMaster or DeepBlue. Computer chess programs can't solve this puzzle!
I'm sorry, but that is just ridiculous. Computer > Humans hands down in a scenario like this. Unless you're playing with rules that the computer doesn't know about, the computer will get it.

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 Post subject: Re: Chess Problem with a twist (Edit: now with 2 hints!)Posted: Thu Nov 25, 2010 11:40 am

Joined: Thu Dec 02, 2004 12:09 pm
Location: Missouri
ppeccin wrote:
Congratulations wwwmwww!
You're the second one to find the answer.

Thanks. I spent far more time on this yesterday then I had planned but I was enjoying it so much I just couldn't walk away from it. I have an idea what bhearn's one slight reservation might be and I'll send you guys another PM shortly to see if I'm correct there.

ppeccin wrote:
Please tell us what you think, and whether you agree that a computer will have trouble solving this puzzle!
(please be careful not to give any hints)

It's been years since I've solved a good chess puzzle and likely a year since my last chess game. I was in a chess club in high school over 20 years ago and did a far bit of this stuff then but I've never used a computer to solve these types of puzzles so I'm not sure what they are really capable of but I suspect they would struggle with this problem.

Here is a similiar type chess puzzle that I've seen before. The problem here is to find the minimum number of moves required for check mate.

Again I'm not sure a computer would give you the correct answer.

I hope a new puzzle doesn't qualify as a hint but this should be a bit easier then ppeccin's puzzle.

Please don't give or discuss solutions here for this new puzzle either as that might spoil some of ppeccin's puzzle. I didn't make this new puzzle so I claim not credit for it but if you solve it and want me to verify your answer PM me but I strongly suspect that if you have the correct answer you will know it.

Carl

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 Post subject: Re: Chess Problem with a twist (Edit: now with 2 hints!)Posted: Thu Nov 25, 2010 12:07 pm

Joined: Thu Dec 02, 2004 12:09 pm
Location: Missouri
edited.. too much of a hint.

Carl

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Last edited by wwwmwww on Thu Nov 25, 2010 12:35 pm, edited 1 time in total.

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 Post subject: Re: Chess Problem with a twist (Edit: now with 2 hints!)Posted: Thu Nov 25, 2010 12:13 pm

Joined: Mon Oct 02, 2006 9:38 pm
Location: Brazil
GuiltyBystander wrote:
ppeccin wrote:
HINT 1: Don't waste your time trying to put this in ChessMaster or DeepBlue. Computer chess programs can't solve this puzzle!
I'm sorry, but that is just ridiculous. Computer > Humans hands down in a scenario like this. Unless you're playing with rules that the computer doesn't know about, the computer will get it.

All right, so try it!
But promise me that you will post here again and tell everybody whether or not your computer was able to get the answer by itself.
Now you owe us this!

Please just don't say anything that could be a hint!

Regards,
Paulo

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 Post subject: Re: Chess Problem with a twist (Edit: now with 2 hints!)Posted: Thu Nov 25, 2010 12:24 pm

Joined: Wed Jan 28, 2009 7:55 pm
Location: Montana
ppeccin wrote:
Questions (if they don't lead to the solution) are welcome.

Do the white pawns move up and the red pawns move down? I was just wondering if there was some orientation trick to the board.

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 Post subject: Re: Chess Problem with a twist (Edit: now with 2 hints!)Posted: Thu Nov 25, 2010 12:27 pm

Joined: Thu Sep 24, 2009 12:21 pm
Location: Chichester, England
No. The board is the correct way around.

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 Post subject: Re: Chess Problem with a twist (Edit: now with 2 hints!)Posted: Thu Nov 25, 2010 12:32 pm

Joined: Thu Dec 02, 2004 12:09 pm
Location: Missouri
Rentlix wrote:
Do the white pawns move up and the red pawns move down? I was just wondering if there was some orientation trick to the board.

In both ppeccin's and my puzzle enough info is given to determine the direction of the pawn's movements.

Carl

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 Post subject: Re: Chess Problem with a twist (Edit: now with 2 hints!)Posted: Thu Nov 25, 2010 1:24 pm

Joined: Tue Aug 11, 2009 2:44 pm
GuiltyBystander wrote:
ppeccin wrote:
HINT 1: Don't waste your time trying to put this in ChessMaster or DeepBlue. Computer chess programs can't solve this puzzle!
I'm sorry, but that is just ridiculous. Computer > Humans hands down in a scenario like this. Unless you're playing with rules that the computer doesn't know about, the computer will get it.

I would agree that in this case, your standard chess computer -- even the strongest, such as Deep Blue -- would be unable to solve this problem. It's not a matter of non-standard rules. I could tell you the reason, but I think if I did, ppeccin might say I was giving too much away.

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 Post subject: Re: Chess Problem with a twist (Edit: now with 2 hints!)Posted: Thu Nov 25, 2010 1:40 pm

Joined: Wed May 13, 2009 4:58 pm
Location: Vancouver, Washington
ppeccin wrote:
GuiltyBystander wrote:
ppeccin wrote:
HINT 1: Don't waste your time trying to put this in ChessMaster or DeepBlue. Computer chess programs can't solve this puzzle!
I'm sorry, but that is just ridiculous. Computer > Humans hands down in a scenario like this. Unless you're playing with rules that the computer doesn't know about, the computer will get it.
All right, so try it!
But promise me that you will post here again and tell everybody whether or not your computer was able to get the answer by itself.
Now you owe us this!
A. I don't know anything about what free programs are top of the line to try this on.
B. I don't have the time or the interest to write one myself.

There is a small finite number of moves available to each player (<50 I think). The computer should easily be able to try all 4^50 moves. Clearly you're using some rare obscure rule that you don't think people will remember and don't expect the programmers to implement. It's really hard to argue without knowing what you're talking about.

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 Post subject: Re: Chess Problem with a twist (Edit: now with 2 hints!)Posted: Thu Nov 25, 2010 1:47 pm

Joined: Mon Aug 18, 2008 10:16 pm
Location: Somewhere Else
GuiltyBystander wrote:
Clearly you're using some rare obscure rule that you don't think people will remember and don't expect the programmers to implement. It's really hard to argue without knowing what you're talking about.

He's not! But the trick he is using isn't something that current chess solvers are programmed to look for.

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 Post subject: Re: Chess Problem with a twist (Edit: now with 2 hints!)Posted: Thu Nov 25, 2010 1:52 pm

Joined: Wed May 13, 2009 4:58 pm
Location: Vancouver, Washington
In that case, can you please post a link to the "official rules" that you're using and make sure they have whatever quirk you're talking about.

I'm quickly losing interest in this problem. I'm a computer scientist so I almost take it as a personal insult that my precious computers can't solve it.

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 Post subject: Re: Chess Problem with a twist (Edit: now with 2 hints!)Posted: Thu Nov 25, 2010 2:08 pm

Joined: Mon Oct 02, 2006 9:38 pm
Location: Brazil
GuiltyBystander wrote:
There is a small finite number of moves available to each player (<50 I think). The computer should easily be able to try all 4^50 moves. Clearly you're using some rare obscure rule that you don't think people will remember and don't expect the programmers to implement. It's really hard to argue without knowing what you're talking about.

Hey, cool down. Its just a puzzle!

GuiltyBystander, I am a software developer and graduated in math. I have over 25 years of programming experience.
So I think I have at least an idea of what I'm talking about.
I have even written my own chess algorithm.

Computer chess programs are designed to PLAY chess, not to solve puzzles. At least normal chess programs. That's why ChessMaster or DeepBlue will never be able to solve this problem. You can try for yourself, and you will probably understand what we are saying.

In this particular case, you are missing the point.
Try to think more "openly". There are dimensions to this puzzle that you are simply not seeing.
It is not simply a matter of trying all possible 2 move combinations for the Whites and responses for the Blacks.

Believe me, there is a solution to this problem, with a proof.
And no, I am not using "obscure" or special rules.
If you know the rules of chess, everything you need to know is on the board.

I can give you a good hint or the complete answer if you're not willing to spend more time trying by yourself.
Just send me a PM asking for it.
But I think you can have some fun once you realize why ChessMaster cannot give you the answer.

Sorry for any trouble!
Peccin

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 Post subject: Re: Chess Problem with a twist (Edit: now with 2 hints!)Posted: Thu Nov 25, 2010 2:29 pm

Joined: Mon Oct 02, 2006 9:38 pm
Location: Brazil
GuiltyBystander wrote:
In that case, can you please post a link to the "official rules" that you're using and make sure they have whatever quirk you're talking about.

I'm quickly losing interest in this problem. I'm a computer scientist so I almost take it as a personal insult that my precious computers can't solve it.

I'm also a computer scientist. Please don't take that as an insult.

Please note that I'm not saying that COMPUTERS in general cannot solve this in anyway.
Of course they can, if you write a specific program to do it. It will take some time but eventually it can be done.

What we are saying is that common Chess Programs and Chess Algorithms like ChessMaster or even DeepBlue will not be able to solve it.

That was part of my motivation to come up with this puzzle.
To create a puzzle that would be impossible for a "cheater" to just open ChessMaster, setup the position and click "Find Mate in 2".

Regards,
Paulo

Last edited by ppeccin on Thu Nov 25, 2010 2:51 pm, edited 2 times in total.

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 Post subject: Re: Chess Problem with a twist (Edit: now with 2 hints!)Posted: Thu Nov 25, 2010 2:45 pm

Joined: Mon Oct 02, 2006 9:38 pm
Location: Brazil
Congratulations Jared!

You're the 3rd to complete the solution!

Now that we have the first 3 I will stop giving congratulations in the public forum, just via PMs!

Thanks,
Paulo

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 Post subject: Re: Chess Problem with a twist (Edit: now with 2 hints!)Posted: Mon Nov 29, 2010 5:50 pm

Joined: Fri Feb 18, 2000 8:50 am
Location: chicago, IL area U.S.A
Just curious, when were you going to share the answer?

I thought I had a proof, but then I found a hole in my logic and now I'm stuck again.
Great puzzle by the way.

-d

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 Post subject: Re: Chess Problem with a twist (Edit: now with the solutionPosted: Mon Nov 29, 2010 11:26 pm

Joined: Mon Oct 02, 2006 9:38 pm
Location: Brazil
I have edited the original post to include the solution.
Please select the hidden text below the board to read it.

Hope you enjoyed!

Regards,
Paulo Peccin

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 Post subject: Re: Chess Problem with a twist (Edit: now with the solutionPosted: Mon Nov 29, 2010 11:47 pm

Joined: Tue Jan 06, 2009 7:23 pm
i got it but i wasnt able to prove in my mind that the king had already moved and prevented his castling, this explained it, never would have gone through all that to prove it though. nice.

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 Post subject: Re: Chess Problem with a twist (Edit: now with the solutionPosted: Tue Nov 30, 2010 5:55 pm

Joined: Fri Feb 18, 2000 8:50 am
Location: chicago, IL area U.S.A
Very well made chess puzzle. I can't believe I missed step 1. I did pick up on step 4 and think had I gotten step 1, I would have gotten further, but I'm still not sure I would have gotten the whole proof. Once again, very well done! Feel free to come up with some more of these types of puzzles.

-d

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 Post subject: Re: Chess Problem with a twist (Edit: now with the solutionPosted: Tue Nov 30, 2010 6:09 pm

Joined: Tue Aug 11, 2009 2:44 pm
For those who like this type of puzzle, the kind of reasoning required is called "retrograde analysis". In a retrograde problem, you have to reason about the history of the game, rather than about the future, as in a typical chess problem.

There is a rich literature of such problems. Two very delightful books of retrograde problems are Chess Mysteries of the Arabian Knights and Chess Mysteries of Sherlock Holmes, both by Raymond Smullyan.

The cover problem from Arabian Knights is, I think, my favorite retrograde problem:

To be perfectly clear, this is a legal chess position that could occur in an actual game, except that the location of the White king is not shown. Where is it?

To solve this puzzle, you will need to know all the rules of chess. I love this problem because it seems to be not too difficult to prove that the position is impossible.

Last edited by bhearn on Tue Nov 30, 2010 8:41 pm, edited 1 time in total.

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 Post subject: Re: Chess Problem with a twist (Edit: now with the solutionPosted: Tue Nov 30, 2010 8:03 pm

Joined: Mon Oct 02, 2006 9:38 pm
Location: Brazil
Very interesting.
When I created this puzzle I had no idea there was a well defined category for its kind.
In fact, until bhearn's answer I had just seen your typical Mate in 2 problems, the ones you have to think only about the future.
But I never looked too much.

This is the first time I made this puzzle public. It was created about 12 years ago, and only a handful of friends have seen it.

Now that I took the time to write the solution in English, I'll look for Chess websites and try to post it somewhere else!

Any of you guys more versed in chess know a good site for chess problems, where I could submit it?

bhearn, about the puzzle on the cover of the book, I don't think I understood it. Do you mean that the White King can only be at ONE specific square of the board and that can be proved?
If that is the case, WOW..... It really seems as it could be at SEVERAL squares with no problem and it would be extremely difficult to exclude all squares but one!

Regards,
Paulo

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 Post subject: Re: Chess Problem with a twist (Edit: now with the solutionPosted: Tue Nov 30, 2010 8:18 pm

Joined: Tue Aug 11, 2009 2:44 pm
ppeccin wrote:
This is the first time I made this puzzle public. It was created about 12 years ago, and only a handful of friends have seen it.

I should say that constructing problems of this type is very difficult. I tried my hand at it when I first read Smullyan's books, more than 20 years ago, and I didn't come up with anything as good as this.

To compose this problem without even being aware of the concept of retrograde analysis is quite impressive!

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 Post subject: Re: Chess Problem with a twist (Edit: now with the solutionPosted: Tue Nov 30, 2010 8:19 pm

Joined: Wed Jan 28, 2009 7:55 pm
Location: Montana
@bhearn I think the answer is the square just beneath the bishop (A3). Here's why:

-The bishop has the king in check, so it must be black's turn.
-The bishop can only have gotten to that square before the rook did
-Since the bishop must have only put the king in check this turn, the white king must have had to move the turn before from check.
-A king can never be adjascent to another king. That means it must have been at B3.
-The only safe place to move the king from B3 out of check is to A3

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 Post subject: Re: Chess Problem with a twist (Edit: now with the solutionPosted: Tue Nov 30, 2010 8:20 pm

Joined: Tue Aug 11, 2009 2:44 pm
ppeccin wrote:
bhearn, about the puzzle on the cover of the book, I don't think I understood it. Do you mean that the White King can only be at ONE specific square of the board and that can be proved?

Yes, exactly!

Quote:
If that is the case, WOW.....

Indeed!

Last edited by bhearn on Tue Nov 30, 2010 8:23 pm, edited 1 time in total.

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 Post subject: Re: Chess Problem with a twist (Edit: now with the solutionPosted: Tue Nov 30, 2010 8:23 pm

Joined: Tue Aug 11, 2009 2:44 pm
Rentlix wrote:
-A king can never be adjascent to another king. That means it must have been at B3.
-The only safe place to move the king from B3 out of check is to A3

Actually C3 is also safe. But please tell me this. If the king just moved from B3, then how did Black put him in check from the rook and the bishop simultaneously?

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 Post subject: Re: Chess Problem with a twist (Edit: now with the solutionPosted: Tue Nov 30, 2010 8:24 pm

Joined: Mon Oct 02, 2006 9:38 pm
Location: Brazil
Oh, I got it!!!

Excellent problem.

I will not put the answer here, but I can say that I do not agree with Rentlix...
I'll send a PM!

Paulo

Last edited by ppeccin on Tue Nov 30, 2010 8:31 pm, edited 1 time in total.

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 Post subject: Re: Chess Problem with a twist (Edit: now with the solutionPosted: Tue Nov 30, 2010 8:27 pm

Joined: Wed Jan 28, 2009 7:55 pm
Location: Montana
ppeccin wrote:
Rentlix: did you just say the King moved from b3 to b1??? Thats 2 squares at once!

Fixed the typo. I meant A3.

@bhearn wow, I didn't think about being checked by two pieces at once. I'll need to do more thinking.

_________________
Andreas Nortmann wrote:
Things like this are illegal.
If not I will pass an appropriate law.

Last edited by Ender Delphiki on Tue Nov 30, 2010 8:34 pm, edited 1 time in total.

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 Post subject: Re: Chess Problem with a twist (Edit: now with the solutionPosted: Tue Nov 30, 2010 8:31 pm

Joined: Tue Aug 11, 2009 2:44 pm
ppeccin wrote:
Oh, I got!!!

I'll send a PM!

Yes!!! You got it. VERY impressive. It took me a lot longer.

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 Post subject: Re: Chess Problem with a twist (Edit: now with the solutionPosted: Tue Nov 30, 2010 8:33 pm

Joined: Fri Mar 06, 2009 9:23 pm
This was a really great problem. I was so lose to solving it. Very interesting!

_________________
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My Shapeways shop

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 Post subject: Re: Chess Problem with a twist (Edit: now with the solutionPosted: Wed Dec 01, 2010 2:34 am

Joined: Fri Nov 04, 2005 12:31 am
Location: Greece, Australia, Thailand, India, Singapore.
Agreed with everyone, nice challenge, with some nice twist.

There was some crazy chess guy back in 1993 when I was
studying under the exchange program in Essen (Germany)
He was waiting for me every afternoon after I finished my
lectures to challenge me in a timed game of chess.

He was a genius and he would be proud of this problem!

Pantazis

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