an unexpected draw

White moves and forces a draw

Originally posted by Mephisto2
White moves and forces a draw

[fen]nB3RbN/1kppppq1/1p4p1/1P3p2/Bp3P1n/4PrbP/2PP1rP1/R3K3 w[/fen]

Wow, that really looks unexpected. All I can think of is 1. c3.

EDIT:No, wait, that's mate
1. ... Rxg2+ 2. Kd1 Rf1+ 3. Kc2 Qxc3#

He, this looks like an interesting problem, got take a deeper look.

EDIT: If you say 'unexpected', then maybe black offered it in this situation, no?

I suppose it has something to do with those strangely placed Bishops on b8 and g8 - but I cannot deduce that, for example, there have been no pawn moves or captures in the last 100 half moves.

The pawn structure has something 'retrogradic' in it, though...

EDIT: If you say 'unexpected', then maybe black offered it in this situation, no?

No, black had no choice.

Originally posted by heinzkat
I suppose it has something to do with those strangely placed Bishops on b8 and g8 - but I cannot deduce that, for example, there have been no pawn moves or captures in the last 100 half moves.

The pawn structure has something 'retrogradic' in it, though...

(also notice the Knights on a8 and h8, and the White Rook on f8, and probably in the same way there must have been something strange going on for Black's Rooks on f2 and f3, and the Bishop on g3.)

Originally posted by Mephisto2
White moves and forces a draw

[fen]nB3RbN/1kppppq1/1p4p1/1P3p2/Bp3P1n/4PrbP/2PP1rP1/R3K3 w[/fen]

1. Ba7 and White claims a draw because of the 50-move draw rule.

There is no reasoning behind this particular move and no valid reason for the claim though.

Originally posted by heinzkat
1. Ba7 and White claims a draw because of the 50-move draw rule.

There is no reasoning behind this particular move and no valid reason for the claim though.

Maybe SwissGambit can astound us with retrogradic proof that this position has been reached with no pawn moves or captures during the previous 50 moves.

I really don't see a move that doesn't lead to mate.

Originally posted by Mephisto2
White moves and forces a draw

[fen]nB3RbN/1kppppq1/1p4p1/1P3p2/Bp3P1n/4PrbP/2PP1rP1/R3K3 w[/fen]

My guess:

White plays O-O-O, and then shows that the fact that he was able to castle implies that the last 50 moves were without captures/pawn moves.

Second thought: this is not very logical - why can't white play any other non-capture, non-pawn move? why does white have to actually castle, since castling is already assumed legal unless proved otherwise? maybe someone (SwissGambit?) who is a retro expert knows: in retros, can white use the fact that he MAY castle (because castling can't be proved illegal) to prove that 50 moves were made without captures/pawn moves?

White plays O-O-O, and then shows that the fact that he was able to castle implies that he hasn't moved his King nor a1 Rook yet.

Which proves there have been no captures during the last 50 moves? Hmm...

OK: the h1 Rook must have travelled then via f1, where the Bishop must have disappeared, so e3 must have been played before that; f4 must have been played too, so that Rf1-f3 was possible. But the Knight from g1 must have disappeared too before Rh1-f1 is possible: perhaps it has been captured by some piece, perhaps it has travelled to h8.

I suppose something like this leads to an imminent 50 moves without captures!? Tough stuff.

Originally posted by David113
My guess:

White plays O-O-O, and then shows that the fact that he was able to castle implies that the last 50 moves were without captures/pawn moves.

Second thought: this is not very logical - why can't white play any other non-capture, non-pawn move? why does white have to actually castle, since castling is already assumed legal unless proved otherwi ...[text shortened]... astling can't be proved illegal) to prove that 50 moves were made without captures/pawn moves?

You are on a good track. And yes, if castling can't be proved to be illegal, then it is a possible move. The question is wether castling vs. another white move makes a difference in the number of moves since the last capture/pawn move.

Originally posted by Mephisto2
You are on a good track. And yes, if castling can't be proved to be illegal, then it is a possible move. The question is wether castling vs. another white move makes a difference in the number of moves since the last capture/pawn move.

This doesn't answer my question - why must white actually castle? Why can't white play any non-capture, non-pawn move, and then argue "in my last move I could have castled, and so..." ?

My point is, that everything that white can prove by castling, white can also prove without actually castling, because the proof follows from the ability to castle - not from the actual castling. The only function of the castling is to prove that the white king & rook never moved; but according to the chess problem conventions, white never needs to prove that.

Originally posted by Mephisto2
White moves and forces a draw

[fen]nB3RbN/1kppppq1/1p4p1/1P3p2/Bp3P1n/4PrbP/2PP1rP1/R3K3 w[/fen]

As other posters have suspected, this one involves both castling and the 50-move rule.

13 White units showing + 3 bP captures = 16 [no spare captures]

Black P captures were axb4 [not axb6?? shutting in Bb8] and h7xg6xf5 [the immediate retraction h7xg6?? shuts in Bg8]. No other captures were made.

White is missing a Q, N and P. The missing P is a2 [no wP caps allowed] and it promoted [a pawn on the a-file could not have sacrificed itself to a bP].

The key is indeed 1.0-0-0, as most solvers would probably guess before doing the grunt work. The main idea is to prove that Rf8 is the original Rh1. If so, we'd have to get him home before retracting f3-f4. First, we must eliminate the possibility that Rh1 was captured somewhere.

possibility 1): axb4
It cannot retracted until White un-promotes on the a-file. To do that, we must somehow get Bg3 to f8, retract g7-g6, retract bK and bQ home, retract Bg8 back to c8, then retract b7-b6, all so we can free the promotion square with Nb6. The problem with this plan is that Bg3 cannot escape until the f4 pawn retracts, which is waiting on the very Rook I hoped to uncapture. Note that Bf1/e2 for White also locks out the Rh1, so the bBg3 cannot escape that way either.

possibility 2): g6xf5
I need to retract Bg3 to f8 and g7-g6 before this uncapture, but we have already established the bB cannot leave in poss. 1) above.

So, Rf8 must be Rh1 by elimination. The problem is that he must somehow get past both Black Rooks. Only by sending all the Rooks to the Queenside (!!) can we buy enough space to accomplish this. The plan goes:

[Counting only Black's moves at first...]
3 Qe5 Bh7-g8 [while wR goes to h6]
6 Kb7-f6 [better to just get him out of the corridor]
1 Bh7 [to let wR go to Qside]
1 Bh2
13 Rf3-b2, Bg8-h7
13 Rf2-a2, Bg8-h7
[now with bR's clear, we count White's moves to get the R home, not counting the actual retraction to a3, since it's part of the same full move as Black's final Ra2]
13 wRa3-f1
---
50 moves

The retraction runs:
1...Bh7 2.Rg8 Qe5 3.Rg7 Bg8 4.Rh7 Kc8 5.Rh6 Kd8 6.Ba7 Ke8 7.Bb3 Kf8 8.Be6 Kg7 9.Bd5 Kf6 10.Rh7 Bh2 11.Rg7 Bh7 12.Rg8 Rg3 13.Rb8 Rg5 14.Rb7 Rh5 15.Bb8 Bg8 16.Rba7 Rh7 17.R7a3 Rg7 18.Rd3 Bh7 19.Be6 Rg8 20.Ba7 Rb8 21.Bd5 Rb7 22.Bb8 Ra7 23.Be6 Ra2 24.Bd5 Rb2 25.Be6 Rf3 26.Rc3 Rg3 27.Rd3 Rg5 28.Rc3 Rh5 29.Rd3 Bg8 30.Rc3 Rh7 31.Rd3 Rg7 32.Rc3 Bh7 33.Rd3 Rg8 34.Ba7 Rb8 35.Rc3 Rb7 36.Bb8 Ra7 37.Rd3 Raa2 38.Ra3 Rb3 39.Ra7 Rc3 40.Rb7 Rb3 41.Ba7 Rc3 42.Rb8 Rb3 43.Rg8 Rc3 44.Rg7 Bg8 45.Rh7 Rb3 46.Rh5 Rc3 47.Rg5 Rb3 48.Rg3 Rc3 49.Rf3 Rb3 50.Rf1 Rc3 51.f4f3

1.0-0-0 is the 100th ply with no pawn move or capture, so White gains a draw by the 50-move rule.

Originally posted by David113
This doesn't answer my question - why must white actually castle? Why can't white play any non-capture, non-pawn move, and then argue "in my last move I could have castled, and so..." ?

My point is, that everything that white can prove by castling, white can also prove without actually castling, because the proof follows from the ability to castle - not ...[text shortened]... ever moved; but according to the chess problem conventions, white never needs to prove that.

White has to castle, not because he needs to prove he can castle, but because he needs to prove the 50-move rule applies!

There are some more complex chess problem conventions relating to conflicting assumptions - for example, what if retro analysis shows that only one side or the other [but not both!] can possibly still have castling rights? Who gets them?

One way of solving the dilemma is A Posteriori. In this type of problem, he who first exercises his rights nullifies the opponent's rights. The same reasoning is in play here.

Great job! Not only to find the solution, but also the explanation is quite rigorous!

Perhaps one extra clarification 1. 0-0-0 allows white to claim the 50-moves rule, as was clearly shown above. If the starting position had occurred via an other way that involved white losing his castling rights, then it can be shown easily that the position could have been reached in far less than 50 moves since the last capture/pawn move (the rather complicated shuffling with the rooks is not needed).