Black to move. How should Black proceed? No computer please.
8/7p/5kp1/4p3/p3rPRP/3K2P1/2P5/8 b – – 0 1
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1. ….Rd6 , 2. Kxd6 h6 .
1. ….Rd6 , 2. Kxd6 h6
1. a3 should work. If 1…Kc3, then Re3+ and neither the king nor the rook can stop the pawn.
For those studying this, don’t make my mistake and spend 15 minutes thinking the board was turned the other way. Sheesh!
My first thought, once I had oriented the board correctly, was that a3 might win, but it doesn’t since white captures with check at e5 and black is forced to capture with the rook and white’s rook can make it over in time to stop the a-pawn:
My second thought was to push h5:
1. …..h5
2. fe5
Here, Ke4 looks losing to me since black will win the pawn race: [2.Ke4 hg4 3.fe5 Ke6-+]. Continuing:
2. …..Re5
3. Ra4 and only white can win this.
My third thought was the check from d4, but I think white can hold it if he selects the right move:
1. …..Re4
2. Kc3!
I will mention the Ke2/Ke3 lines later since that was how I found the right solution. Continuing:
2. …..Re4
I tried everything else here, and nothing I looked at seemed promising. White is threatening to play fe5+ winning the rook, so black needs to either play Re4 so that he can capture at e5, move the rook out of the line of discovered attack, or move the king so that fe5 doesn’t enforce check. The clearest line I can find for black is to just return the rook to e4. Continuing:
3. fe5 Ke5 (Re5 no better)
4. Re4
White might do better with Rg5, but it seems drawish to me, too. Continuing:
4. …..Ke4
5. Kb4 Kd4
6. Ka4
Everything else seems a bit dangerous to my eye, but I didn’t look in detail at this since I already had a better idea for black’s first move. Continuing:
6. …..Kc3
7. Kb5!
Probably forced. Continuing:
7. …..Kc2
8. Kc4!
Also probably forced. If white tries the shorter path to the h7 pawn, I think black wins: [8.Kc5? Kd3! 9.Kd5 Ke3! and both white pawns will fall before white can liquidate h7 and g6.]. Continuing:
8. …..Kd2
9. Kd4! Ke2
10.Ke4! Kf2
11.Kf4! Kg2 (nothing better)
12.Kg5
The clearest draw for white. Here, g4 should draw after black plays Kh3. What white might want to avoid is 12.Kg4 since black plays h6 followed by Kh3- I still think this will be drawn, but I didn’t do the full analysis on that line- it reduced in my line to a K + P vs K ending for black, but white could get the opposition at g2 with the black pawn at g5, and that is drawn. Continuing:
12. ….Kg3
13. h5! and white will liquidate the black pawns.
In my next comment, I will discuss a more promising approach for black.
In my previous comment, I discussed some of the rook moves along with the immediate push of a3. The idea of pushing a3 is that the white king is right at his limit in distance from the pawn to stop it, and white’s rook is hemmed in by the white f, g, and h-pawns. However, when pushing a3, white has the resource of fe5+ to break his rook out of jail. In one of the lines where black checks from d4 on the first move, I found a king move that wins for black if the white king has moved to e2 or e3. It was clear immediately this move is a forced win if played immediately:
1. …..Kg7!!
The idea for moving the king is to prevent fe5 by white. Playing 1. …Ke6 doesn’t work due to Ke4: [1. …Ke6?? 2.Ke4! a3 3.Rg5 a2 4.Re5 with check! and the white rook makes it to a5 just in time. Also, 1. …Ke7 loses for the same reason. Playing Kf7 loses to a key check from f4: [1. …Kf7 2.Ke4 a3 3.fe5 a2 4.Rf4! and 5.Rf1 comes in time.]. With 1. …Kg7, black retains a critical tempo for pushing the a-pawn. Continuing from move 1 above:
2. Kc3
Nothing better I can see. The rook is immune: [2.Ke4? a3! and the pawn will queen]. The rook can’t stop the pawn, so the white king must try. Continuing:
2. …..h5
The clearest of the lines to me. I think h6 will win, too. I am not as sure about a move like a3 or Re3. Continuing:
3. Rg5 ef4!
4. gf4
If there is a better move, I don’t see it. White cannot allow black a second advanced passed pawn either, so he must take it. Continuing:
4. …..Rf4 and black will win the h-pawn too. This is more than enough to win for black.
1… Rd4+ and 2… E4 White cannot stop either pawn A or pawn E
Very interesting puzzle, dear Susan. Where does it come from! All in all, the solution is very contorted and I couldn’t find it. Let’s see if the sharpest carbone-based brains will solve it.
And yes, the solution is unique and non trivial, not as beautiful and as flashy as studies, but very difficult and those who immerse their thoughts deep enough into this position will be very well rewarded.
1…. Kf7
if 2KxR, c3
if 2Ke3, Re3+
if 2h5, g5
Anonymous commenter at 4:19 PM,
Don’t know if Susan will publish this early, but
1. …..a3
2. fe5! Re5
3. Ra4 will stop the a-pawn. I don’t think there are any winning chances for black after this, and not much for white either, but he would at least have some play.
Unknown,
I toyed with that line, too, but it fails. The key line is
1. …..Rd4
2. Kc3 e4
3. Kd4
Here, Rg5 is probably a drawish line, but I am not completely sure. However, it is irrelevant since Kd4 wins outright. Continuing:
3. …..h6 (to prevent Rg5)
If 3. …a3, black plays Rg5 and wins easily. If black plays 3. …e3, white captures at e3 and can clear the path for the rook by playing 5.f5 if black has tried 4. …h6, or can play 5.Rg5 if black has played 4. …h5. Continuing:
4. Ke4
Lots of winning moves here, some transpose, some don’t. Here 4.f5 or 4.h5 nearly as good. Continuing:
4. …..a3 (nothing else now)
5. h5!
Now f5 might not win since black captures with check and the white king will have to retreat to d3 and c3 to stop the a-pawn. A likely draw based on a crude move count I just made-white can win at a3 and queen the c-pawn while allowing black to capture both kingside white pawns and queen the g-pawn just after white queens giving likely drawn Q+RP vs Q ending. With h5, white threatens Rg6+ followed by Ra6. Black has no counter that doesn’t just hand white the tempii to clear the 4th rank for the rook, or to open the path to g8 for the rook. Continuing from move 5 above:
5. …..g5 (gh5 6.Rg8; a2 6.Rg6+)
6. fg5+ hg5
7. Ke3 and white wins easily.
How about just a waiting move like 1… Kg7, trying to exploit the fact the white rook is so out of play and threatening to promote with a3
2. Kxe4 a3 (winning)
2. Kc3 Re3+
3. Kb4 a2 (winning)
2. c4 a3
3. Kc2 Rxc4+
4. Kb1 e4 (Black should be winning with two passed pawns and the white rook out of play)
1. ….Rd6, 2.
1. …Kg7, 2.Kxe4 a3 , 2.Kc3 h5 , etc.
1. … Kg7 , 2. Kxe4 a3 ; 2.Kc3 h5; etc.
The chess board is indeed upside down!! As A1 should be seen at the bottom left normally when the chess board is not upside down.
1…Kg7 getting out of any possible checks from black. Other moves can’t win.
Re3+ It´s over
If
KxR, a3
Correction
1. … Kf7
if 2.KxR,a3
if 2.h5,g5; 3.Rxg5,a3; 4.Kc3,Rd3+
if 2.Kc3,h6; 3.Kb2,Rd4; 4.Ka3,e4
Carlos, 1…Re3+ fails:
2.KxR, a3
3.PxP+, K any
4.Ra4
Black has to get his king away from the pawn check and also keep the white rook trapped. Hence 1…Kf7.
Yancey,
I think your 1…Kg7 is the right idea, but it fails to 2.h5 followed by 3.Rh4 and 4.Rh1.
Black’s 2….g5 to prevent the White rook maneuver doesn’t work, because R takes with check and gets back to h1 in time.
That’s why 1…Kf7 is best.
@Walter
1…Kg7 is the only move that wins.
1…Kf7 even loses
Your two oversights are:
1..Kg7 2.h5 (“followed by Rh4 and Rh1”) but 2…a3! 3.Rh4 (3.Kc3 doesn’t save because of the patzer-like move Re3+, and White must get out of the square by 4.Kd2 a2 and 0-1) and now?
3…Re1!! and the a pawn queens.
1…Kf7 2.Kxe4 a3 3.fxe5 a2 4.Rf4+ tempo win Δ5.Rf1
So, interestingly, you suggested a manoeuvre Rh4-h1 that doesn’t work, and overlooked a similar manoeuvre Rf4+-f1 which works!
I must admit that 3…Re3+ was far from evident and is not a standard flashy refutation but a hidden intermediate move!
In the same vein, 4.Rf4+ is not evident.
Morality: check your checks!
Walter,
I covered your line in my comment above outlining Kg7. First, let’s discuss Kf7 again:
1. …..Kf7??
2. Ke4! a3 (nothing else to try)
3. fe5
And now white is threatening Rf4 with check, followed by Rf1 covering a1 in time to stop the a-pawn, so 3. …a2 can’t win for black. If he attacks the rook with h5, white still plays Rf4+, and playing g5 won’t help since white can just move the king off of the 4th rank allowing Ra4 to stop the pawn. White wins all scenarios. Now, lets move to Kg7 and your ideas for refuting it since I did overlook that line in my haste the other night:
1. …..Kg7!
2. h5 a3!
3. Rh4 Re1! and white will lose his rook to stop the pawn.
Now, at move 3 in this line, white could take at e4 to prevent Re1, but this gives up the tempo required for the Rh4-Rh1 maneuver:
1. …..Kg7
2. h5 a3
3. Ke4 a2 and white has no time for two rook moves to the first rank.
1. …..Kg7 does win.
Yancey,
OK, I’m convinced.