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        riddles >> hard >> A CHESS PROBLEM
        
(Message started by: pcbouhid on Nov 26^th, 2005, 8:00am)

Title: A CHESS PROBLEM
Post by pcbouhid on Nov 26^th, 2005, 8:00am

This position was achieved in a normal chess game. What piece is "?"?

Title: Re: A CHESS PROBLEM
Post by Joe Fendel on Nov 30^th, 2005, 8:06am

I like retrograde chess puzzles. This puzzle looks familiar. Is it one of Smullyan's?

A major key to solving these problems is to know that a pawn reaching the last rank can promote to a bishop, rook, knight, or queen (and not just a queen, as most believe). Why someone would promote to a piece other than a queen is not at issue - it's a legal move. (In fact, Smullyan has produced cases where the only winning move is to promote to a Knight, and - in one ingenious reading of the rules - a case where the only winning move is to promote to a piece of the other color!)

Here are a few hints:

[hide]Who moved last[/hide]?

[hide]What could have possibly been a legal last move[/hide]?

[hide]Simultaneous check is impossible. How does that limit the options for the unknown piece[/hide]?

[hide]Where did the bishop that began the game on F8 go[/hide]?

[hide]What pieces were captured by black pawns during the game so far[/hide]?

Title: Re: A CHESS PROBLEM
Post by pcbouhid on Nov 30^th, 2005, 9:55am

Joe, I can´t assure you that it´s a Smullyan´s. I found it in a site, with two others problems, much more easy. This, indeed, it´s a hard one.

Reading your hints, I think you already solved it.

Title: Re: A CHESS PROBLEM
Post by Joe Fendel on Nov 30^th, 2005, 10:38am

One I haven't solved, though, is Elkies' URG:

6. gxf8N mate

(In other words, White's sixth move was to capture a piece on f8 with his pawn at g7, promoting to a Knight and checkmating Black.)

Reconstruct the entire game.

Title: Re: A CHESS PROBLEM
Post by pcbouhid on Dec 1^st, 2005, 6:15am

Sorry, Joe, but though a very good chessplayer(that once I was, but I don´t play chess since the final of the eighties), by the time when I even played postal chess (before computers programs), I never studied retrograde analysis.

I still have dozzen of books about chess, none of them about this subject.

It´s quite interesting, but I don´t know if now I can make it. If you don´t mind, I´ll leave your problem for those who are still "in the race".

Cheers.

Title: Re: A CHESS PROBLEM
Post by SMQ on Dec 1^st, 2005, 11:01am

We solved this one over in Easy (http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/YaBB.cgi?board=riddles_easy;action=display;num=1121258196) a few months back. ;)

--SMQ

Title: Re: A CHESS PROBLEM
Post by Margit on Dec 2^nd, 2005, 3:54am

I think I am there :
[HIDE]
Only legal move for white was
Pc7 x <whatever>d8 = R
Let's look at <whatever>
It can not be BR or BQ as white would have
been in check and there is no place that
either the BR or BQ could have come from.
Therefore it is either a BN or BB.
In either case, it has to be a promoted
piece (Knight is obvious althugh it could be an
original knight, original bishop
at f8 can not have moved).

Now lets look at the ? piece.
It can not be BR or BQ as that gives illegal
simultaneous check.
It can not be BP as we have proved that black promoted.
And it can not be BR or BN as white has just
captured the promoted piece.

Therefore it is not a black piece.

It is not a white pawn as white has just promoted.

This leaves WR, WQ, 2 x WN and 2 X WB.

5 of these pieces have been taken by black pawns.

Lets look at the black pawns.
The pawn at a6 came from b7 capturing something.
The pawn at c4 came from f7 capturing at e6, d5, c4.
The promoted pawn came from h7 and captured at g6. It then ran the g file to promote. The WP at g3 must have captured from f2.

This accounts for blacks capture of 5 white pieces
BUT note that all captures were on WHITE squares;
therefore the only piece that can not have been
taken by black is the WKB. ? = WKB.
[/HIDE]

Title: Re: A CHESS PROBLEM
Post by pcbouhid on Dec 2^nd, 2005, 5:46am

Margit, [hide]I´m impressed!!!!![/hide]

Title: Re: A CHESS PROBLEM
Post by Margit on Dec 2^nd, 2005, 7:22am

:D

I am just wondering if this actually qualifies as a retrograde. The only actual move you need to know is the last white one. Everything else can be deduced. Maybe TB/SMQ can call that.

On the link that SMQ posted, I notice that TB
posed a problem that was never answered -
"Now construct a game which ends with 6. BxR (on c4) mate"

Title: Re: A CHESS PROBLEM
Post by Margit on Dec 2^nd, 2005, 1:54pm

Here is a twist on the original problem.
Replace the White Rook at d8 with a White Bishop.
What can we now say about the piece marked "?". :-/

Title: Re: A CHESS PROBLEM
Post by Joe Fendel on Dec 2^nd, 2005, 2:37pm

If it's a bishop instead of a rook, [hide]then certainly the ? could still be a white bishop if we assume the d8-bishop was just promoted as before.

But since the bishop could have just moved there as a bishop from c7, and may not have captured anything, that kills much of our analysis. I don't think we can rule out any piece, except a black queen or rook for simultaneous-check reasons as before.[/hide]

Title: Re: A CHESS PROBLEM
Post by Margit on Dec 3^rd, 2005, 12:59am

There is a mistake in my original solution.
Of course, [HIDE]WKB[/HIDE] should be [HIDE]WQB[/HIDE] :-[

Title: Re: A CHESS PROBLEM
Post by Margit on Dec 3^rd, 2005, 2:27am

Yes, Joe.
Maybe we can restate the problem :
Replace the White Rook at d8 with a White Bishop.
"White's last move uniquely determines the piece marked '?'. What is '?' ?".
I like that !
More choices over the original.

Although as you say -
[HIDE]If the bishop just moved c7-d8, I can not see that we can deduce anything. However, if the bishop captured something on d8, that gets interesting.[/HIDE]

Title: Re: A CHESS PROBLEM
Post by Margit on Dec 3^rd, 2005, 2:45am

Does this work as a variant ?
Replace the White Rook at d8 with a White Bishop.
Put a White Pawn at f3
"White's last move uniquely determines the piece marked '?'. What is '?' ?".

Title: Re: A CHESS PROBLEM
Post by Grimbal on Dec 3^rd, 2005, 12:37pm

on 12/02/05 at 03:54:52, Margit wrote:

I think I am there :
[HIDE]5 of these pieces have been taken by black pawns.
...
The promoted pawn came from h7 and captured at g6. It then ran the g file to promote.
[/HIDE]

[hide]How can you tell the 5 pieces were taken by black pawns, and not another black piece?

How do you know the pawn from h7 captured at g6 and not, say, at g2?[/hide]

Title: Re: A CHESS PROBLEM
Post by Joe Fendel on Dec 3^rd, 2005, 2:47pm

on 12/03/05 at 12:37:38, Grimbal wrote:

[hide]How can you tell the 5 pieces were taken by black pawns, and not another black piece?

How do you know the pawn from h7 captured at g6 and not, say, at g2?[/hide]

[hide]Where did the pawn currently at a6 come from? It must have been b7, capturing once on a6 (a white square). How about the pawn at c4? It must have been f7, capturing on e6, d5, and c4 (all white squares).

(This may not be immediately obvious. Consider this - the 6 black pawns currently in the a, c, d, and e files must have come from a7 through f7, because the g7 and h7 can't reach any of their squares. Of those six pawns, only one is on a square reachable by the original f7-pawn, the one currently at c4).

Add the capture that the h7 pawn used to switch files and that totals 5 captures by black pawns.

Knowing that the h7 pawn captured at g2 is a little more subtle. The pawn currently on g3 came from either g2 or f2. Suppose it came from f2. Then where did the pawn which just promoted to the rook at d8 come from? Must have been g2, since none of the other pawns could have come from g2. How many captures must these two pawns have made altogether? 1 by the f2-pawn (on g3) and 5 by the g2-pawn (4 to get to the c-file, and 1 to promote to the rook). Now add in the capture of the bishop on it's home square of f8. That totals 7 captures. But since black is only missing 6 pieces, that's impossible.

Thus the g3 pawn came from g2. If the h7 pawn captured before g2, it couldn't get around the g-file pawn. Thus it must have captured on g2 (a white square).[/hide]

Title: Re: A CHESS PROBLEM
Post by Grimbal on Dec 3^rd, 2005, 4:05pm

But Margit said:
[hide]The promoted pawn came from h7 and captured at g6. It then ran the g file to promote. [/hide]
???

The rest is clear now.

Title: Re: A CHESS PROBLEM
Post by Joe Fendel on Dec 3^rd, 2005, 4:22pm

on 12/03/05 at 16:05:54, Grimbal wrote:

But Margit said:
[hide]The promoted pawn came from h7 and captured at g6. It then ran the g file to promote. [/hide]
???

So she did! That was a minor error in her reasoning, you're right!