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        riddles >> medium >> What Piece is Missing? (Chess)
        
(Message started by: ThudanBlunder on Apr 27^th, 2008, 3:34pm)

Title: What Piece is Missing? (Chess)
Post by ThudanBlunder on Apr 27^th, 2008, 3:34pm

The position during a game of chess was as below.
But a piece has been knocked off h4.
What was the piece?

Title: Re: What Piece is Missing? (Chess)
Post by Wardub on Apr 27^th, 2008, 5:55pm

I have no idea, but I really like these problems so I encourage you to post more.

Anyways back to the riddle.
Heres what I have found so far.
[hide]
1. The black bishop couldn't have moved because the 2 pawns blocking them haven't moved. It is also missing.
2. The last move played was by white, And I think it was pawn on c7 took a knight on d8 and was promoted to rook. The piece on d8 couldn't be a rook or queen otherwise white would be in check. And the black bishop didn't move. So I think its a knight.
3. It looks like the black pawn on c4 must have come from f7.[/hide]

Honestly this looks really confusing. It looks like it could be a number of pieces except a white pawn, or black rook or black queen. I'll give it a little more thought.

Title: Re: What Piece is Missing? (Chess)
Post by ThudanBlunder on Apr 27^th, 2008, 6:57pm

on 04/27/08 at 17:55:46, Wardub wrote:

I have no idea, but I really like these problems so I encourage you to post more.

I have posted lots in the past, the last one being this (http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/YaBB.cgi?board=riddles_easy;action=display;num=1199142831).

on 04/27/08 at 17:55:46, Wardub wrote:

So I think its a knight.

Where did it come from?

Title: Re: What Piece is Missing? (Chess)
Post by Wardub on Apr 27^th, 2008, 7:03pm

looks like the pawn on h7 must have been promoted because there are 2 knights on the field. I'm not sure but it might have been a promoted bishop instead of knight. Anyways I know there is a promoted piece for black and white.

Edit: Thundan look at the problem I posted "Chess: place the king". it got moved to easy.

Also Black has captured more than 4 pieces. Because the pawn on a6 has caputered 1 and the pawn on c4 has captured 3 and I have proved that the pawn on h7 gets promoted. But there is still a white pawn on the h file so it had to have captured atleast 1. So 5 pieces.

Of the 5 white pieces, we still have 7 pawns and a promoted pawn, so we know that none of the pieces black took are pawns. We also have 1 rook still on the board. So the 5 white pieces must come from this combination: 2 bishops, 2 knights, 1 queen and 1 rook.

2nd edit. If the pawn originally on h7 took more than 1 piece then we know that the missing piece is black. Because it leaves no more white pieces.

Title: Re: What Piece is Missing? (Chess)
Post by Wardub on Apr 27^th, 2008, 8:44pm

I think I got it.
[hide]Answer: White's dark squared bishop.
Reasons:
We know that at least 5 pieces of whites are taken from pawns. The only way for exactly 5 pieces to be taken is if, the h7 pawn moves to h3 captures at g2 and promotes at g1. This leaves 1 white piece.

Now back to Black. The only pieces that could be there are blacks dark squared bishop or knights, otherwise white would be in check and we would have an impossible position. Earlier I proved that one black pawn was promoted to a knight. Also White has captured a knight when he promoted his pawn. And there are still 2 knights on blacks side. So it would have to be black's bishop. But neither of the pawns that allow him to move have been moved. So this means black can't have a piece there.

Now if Black can't have a piece there, that means black must have captured 5 pieces. If you notice, all the captures must occur on light squares. Of the 6 remaining white pieces only 1 can't move on light squares. That means the 5 captured pieces must have been the 2 knights the light squared bishop, 1 rook and 1 queen. Leaving 1 white dark squared bishop available. So it must be it.
[/hide]

Title: Re: What Piece is Missing? (Chess)
Post by Hippo on Apr 28^th, 2008, 5:47am

I was rather sure the problem was already presented here. There are small gaps in Wardub reasoning, but the result is OK.

[hide]Last move was c7xd8R capturing either bishop or knight. As 2 knights remain on desk and bishop from f8 never moved (Pe7,Pg7) (and was captured by something else than pawn) the missing black pawn was promoted. The figure of promoted kind was captured on d8. So remaining black pieces are rooks, queen and light square bishop. First two will check the white king and the last cannot stand on dark square. So we are looking for white piece. And there were only 5 captures of white pieces. 4 of them are forced on light squares a6,e6,d5,c4 and the remaining one must be on light g2 to allow promotion of the h7 pawn. One of 6 missing white pieces cannot stand on these 5 squares - the dark squared bishop, so this is the figure lost on h4.[/hide]

[edit]
There is a bug in reasoning ... promotion of h7 by only one capture means there was h3xg2 only in the case g3 pawn originates in g2. The possibility g3-g2 followed by f2xg3 should be avoided. But f2xg3 requires g2 to be promoted by c7xd8R and 5 black pieces whould be captured by white pawns. But only 4 are available ( Q,R,R,Bc8 ).
[/edit]

Title: Re: What Piece is Missing? (Chess)
Post by ThudanBlunder on Apr 29^th, 2008, 11:52pm

on 04/27/08 at 17:55:46, Wardub wrote:

I have no idea, but I really like these problems so I encourage you to post more.

Here is a nice 'minimalist' one:

Title: Re: What Piece is Missing? (Chess)
Post by Barukh on Apr 30^th, 2008, 8:41am

Seems like [hide]Kd1xNc1[/hide]. ???

Also seems like a deja-vu.

Title: Re: What Piece is Missing? (Chess)
Post by Wardub on Apr 30^th, 2008, 1:29pm

on 04/29/08 at 23:52:31, ThudanBlunder wrote:

Here is a nice 'minimalist' one:

Yea I have seen that one before. If you don't mind I'll post another. Hopefully it hasn't been posted here before.

Find the least amount of moves to reach this position.

http://i230.photobucket.com/albums/ee177/Wardub/Chess/Mortimer1.gif

Title: Re: What Piece is Missing? (Chess)
Post by ThudanBlunder on Apr 30^th, 2008, 2:16pm

on 04/30/08 at 08:41:10, Barukh wrote:

Also seems like a deja-vu.

It was for Wardup.

Title: Re: What Piece is Missing? (Chess)
Post by Hippo on May 1^st, 2008, 1:31am

It seems like [hide]1. Nf3 e5 2. Nxe5 Ne7 3. Nxd7 Nec6 4. Nxb8 Nxb8[/hide]

Title: Re: What Piece is Missing? (Chess)
Post by Wardub on May 1^st, 2008, 1:22pm

Correct Hippo.

And its Wardub, not Wardup. ;)

Title: Re: What Piece is Missing? (Chess)
Post by Hippo on May 2^nd, 2008, 1:36am

Oops, there is a gap in the reasoning for the first puzzle ... we must also prove the promoted pawn started on f2 not on g2!
But there is not enough black pieces to be captured by pawns (except the last one only 4 ... QRRB ... 3 are sufficient for f2 and 5 are required for g2). ... edited above