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Seems to be a case for underpromotion. I did’t calculated this in detail but would give 1. d8N+ a try. I don’t see a defense for Black leading to more than an endgame K+R vs. K+N.
The study is cooked:
1.Rh7 Qxh7 2.d8=Q Nxd8 3.Rd7+ Ke6! wins for black (4.Rxh7 Nf7+ 5.Kh4 Bd1) whereas the intended solution is 3.- Kg8? 4.Rxd8+ Kg7 5.Rd7+ Kh8 6.Rd8+ Qg8 7.Kh6 Qxd8=.
At best, black can only hope for a draw in this position. A rook sac and then a pawn promotion should bode well for black. For example,
1. Rh7! Qxh7
2. d8=Q Nxd8
3. Rd7+ Kg8
4. Rxd8+ Kg7
5. Rd7+ Kg8
6. Rxh7 Kxh7 draw.
White will be lucky to hold this to a draw. Black is up too much material, and even if White promotes the d-pawn, then Black only loses the knight. Black would still be up a bishop and a pawn. The tempting 1. d8=Q is busted by 1… Qe5+, so White has to look for a different first move. What in blazes could there be?? There are no constructive moves for either the rook on d3 or the White king, and underpromotion of the d-pawn accomplishes nothing. So it has to be the rook on h6 that moves. I have to admit that this is the sad way it occurred to me that white’s first move might be Rh7. And lo and behold, I do believe that is the correct 1st move. White is still going to be very lucky to hold this position to a draw.
1. Rh7 Qxh7
2. d8=Q Nxd8
3. Rd7+ Kg8
4. Rxd8+ Kg7
5. Rd7+ Kh8
6. Rd8+ [ 6. Rxh7+ loses ] Qg8 [ the only try for a win now ]
7. Kh6 [ 7. Rxg8+ loses ] and if 7…. Qxd8 STALEMATE!
And, of course, that must be the point of this problem.
So if Black wants to win, she does better to abandon the queen earlier:
1. Rh7 Qxh7
2. d8=Q Nxd8
3. Rd7+ Ke6
4. Rxh7
Now, Black has the advantage. Maybe not a big one, I admit, but the game is still very much alive.
1.Rh7! Qxh7 2.d8=Q Nxd8 3.Rd7+ Kg8 4.Rxd8+ Kg7 5.Rd7+ Kh8 6.Rd8+ Qg8 7.Kh6! Qxd8 stalemate
I thought this was very tough. It took me over 30 minutes to find this line:
1.Rh7 Qxh7 2.d8Q Nxd8 3.Rd7+ Kg8 4.Rxd8+ Kg7 5.Rd7+ Kg8 6.Rd8+ with a draw.
– SS
I think, white should have to play to draw on this way:
1,Rh7 Qxh7
2,d8=N+ Nxd8
3,Rd7+ Ke8
4,Rxh7
and white has to give sacrifiezed his rook on h6 for bishop and pawn!
Best from Hungary
I don’t see anything better for white than 1. d8N+ N:d8 2. Rd7+ Kf8 3. R:g7 K:g7 4. R:h5 and draws
The position is – as far as I see – very complicated. After
1. d8N+ Black needn’t play Nxd8 but can play Ke8. However it might be the best solution anyway it is not easy to see the best continuation for both players now. Perhaps
White plays
2. Nc6 in order to avoid Queen checks on e5 or e7. But what will come after a Queen move to b2 for example or bishop moves (to e1)?
I have no board and no artificial intelligence with me, so I just suppose that Black can come in danger if he likes to avoid 1. Nxd8 with that draw that you other guys have predicted anyway.
Dan from Germany
Beautiful stalemate.
It’s highly interesting. Here are my two cents from a 2 min look
Line 1: 1. d8+(N) Nxd8 2. Re7+ Kf8 3. Rxg7 Kxg7 Rxh5 gxh5 etc, with a draw
And hence Nxd8 is wrong. Problems arise when the K moves to e7 or d7 (Kf8 obviously fails to Ne6+)
Line 2: 1. d8+ (N) Ke8 2. Nc6 and now black seems to be in zugwang. The Q can’t move … Say Qc7 Rh8+ Ke7 (say) Rh7+ wins Q and probably wins for white. The knight shall not move either 3… Nc5 4. Rh8+ Qxh8 5. Rd8+ followed by Rxh8 and Rxh5 etc. Also, if not Qxh8 then we have
3 … Nc5 4. Rh8+ Ke7 5. Nc6+ Kf7 (Ke6 6. Re8+ and mate soon after) with perpetual.
Hence the only line is Ke7, which seems problematic for white. I can seen 2… Ke7 3. Nc6+ Ke6 4. Re3+ Kd6 5. Re7 Qb2 but it needs resolution.