Exact Proof Game

An "exact proof game" is a type of retrograde chess problem in which the solver attempts to completely reconstruct, move by move, the history of the game.

I don't know if this type of problem is of any interest here.  It will most likely involve a team effort.  So I post it with no expectations.  Or in the words of Rod Serling in those Twilight Zone marathons:  "Presented for your consideration."

Here's the position.  From this position, and the stipulation that it has been reached in a regular game of chess in 18.5 moves, the challenge is to completely reconstruct the game's move history.  ("18.5 moves" means that the position shown is immediately after white's 19th move.)  Good luck.

Please feel free to add comments as you make progress toward a solution, so that the collection of insights into this problem grows.

Note:  I did not compose this problem.  I will reveal the author when it is solved.

Amy

There is definitely interest in this type of thing here; derUbermensch has been posting some deductive puzzles and they've been received quite well; there are a group of people, notably TheGrobe, dsarkar, daxelson, and others, who have been working on them. Furthermore, if none of them are interested in a proof game (which hasn't exactly come up yet) then I definitely am. I will be working on this when I get the chance, a little bit later today probably.

No-idea what to play as black, i assume though, Rxh7?

Okay - first piece of analysis - Black's men are all on their original squares - which means that either one of them just returned to his orignal square, or white's last move captured a pawn or piece that was out wanderin'.

This is a retrograde problem.  The idea is to reconstruct the past history of this game.

And here's how we're gonna solve this thing: Wite has made exactly 19 moves.  What were they? The pawn on a7 required at least 4 moves; the pawns on d4 and f4 required at least 2 more.  The queen needed two moves to get to her current position. The knights require at least three moves to get where they are, the white bishop needs only one move. The white king needed two moves to reach his current position.  The rooks - hmm - the one on h7 needed four moves; the one on g1 needed one. And that, my friends, is 19 moves.

Which means that the white king-side bishop and both missing white pawns were killed on their original squares.

 I think white´s 19th move was bxa7...

Furthermore, (and for clarity) the a7 pawn began as the c-pawn, white has played 0-0, Kh1, and Rg1 (in that order, possibly with other moves between). White also played c4, d4, f4, Nf3, Nbd2, Nf1, Be3, two queen moves, and four more rook moves. Black has lost the a, d, f, and h pawns as well as the light-squared bishop. They must have been captured only by the white moves listed above. Furthermore, white's missing pieces - the e-pawn, g-pawn, and light-squared bishop must all have been captured on their original squares.

Also, the f1-bishop, and I would guess the g-pawn and quite possibly the e-pawn, were captured by black before white castled, probably by black's missing bishop...

Slight revision to the count.  Since castling moves both king and rook, I think there be an extra move available . . . that is, the rook can come "out" of the corner and the king can make his first move toward the corner as part of the same move.

Also, How do the black d and f pawns get captured?  Don't seem to be enough moves for that . . .

actually your original count was correct. You had two errors which canceled out. You originally stated that the king only needs 2 moves, which is wrong (from e1 to h1, 3 moves), and then you forgot about castling which saves another move. So your errors canceled out and the original count was correct.

this puzzle is very tough, I can't seem to get it, keep on getting it on 20th move. 

Is there any evidence for promotions on either side?

Ooh, you had to post this while I'm at work?  A very interesting problem.

I'll have to wait until the end of the day before I can take a look.  Good luck in the mean time.

Grobe - If the king moves from e1 to g1 by castling, then to h1, that's two moves.

The h1 rook can reach h7 with three more moves - f3, h3, h7.  Total moves to get the king and h-rook in position: 5. My original count was 6; only five are really needed, for a total of 18 - which means there's one "extra" move available.

If the king does NOT castle, then the king needs three moves, the rook 4.

The other pieces need a total of 13 moves, so white HAD to castle kingside - otherwise, the position requires 20 (vs. 18) moves.

There is no way for the rook to maneuver f3, h3, h7. To castle the g1 knight would have had to move. If the knight isn't on f3, you are going to have to use more moves. Therefore the rook needs 4 moves to get to h7. 

You're right, of course - something like e1, e5, h5, h7.  But that accounts for all 19 moves.

c2-c4-b5-b6-a7 (4)

d2-d4 (1)

f2-f4 (1)

Qd1 - somewhere - h3 (2)

Ke1 - 0-0 - h1 (1.5)

Rh1 - 0-0 - e1 - e5 - h5 -  h7 (4.5)

Nb1 - d2 - f1 (2)

Ng1 - f3 (1)

Bc1 - e3 (1)

Ra1 - g1 (1)

The queen move probably captures the black f-pawn on f3 . . .

Thanks to everyone who has contributed so far.  I'm always amazed by the talented individuals on chess.com.

Please keep working at it, but if no progress is being made in a reasonable length of time, I will publish the solution.

Amy

I believe there is an error in the move count. Unless it was a game with piece odds ; )  The white pieces need at the very least 19 moves to reach the position, which leaves out time to capture the d and f pawns. I really want to be proven wrong, as it would be one nice piece of chess art if it holds up. When do we get the solution?

OK, I will publish the solution as a complete game sometime today.

Say, noon Pacific Time (20:00 UTC).  So you still have about 5-1/2 hours from the time I posted this comment to get in a solution, although it does look like everyone has given up.

Amy