The theory of the “square of the pawn” applies here, that is, the King would be able to catch up the pawn if in its next move, it enters the square bound by the following points: (1) square where the pawn is located; (2)the queening square; (3) the square in the 8th rank diagonally connecting to point 1; and (4) the square in the rank where the pawn is located that intersects 1 and 4. Hence, the only move to draw would be 1. h5 as 1. hxg5 fails to 1…fxg3.
Oh, it says “White to play and draw”! I broke my head trying to find a win 🙂
Any king move loses. Any pawn capture loses too. So by process of elimination, only g4 and h5 look feasible. h5 also loses due to Qa1+ and Qxh8. Hence the only realistic drawing chances are with g4. I would play:
Just counting, and taking note of the fact that the white king is sitting on the a1/h8 diagonal, I think white has to play g4 here. If white passes on the first move with h5, black takes at g3 and queens the half move before white does at h8, and then skewers from a1 to win the new white queen. If white takes at g5 on the first move, black again queens at g1 a half move ahead and covers the g8 square. Finally, if white takes at f4 on the first move, black can take at h4 and black’s king can then play to c6/c5 to stop the white f-pawn. After 1. g4 gh4 2.g5, black can queen at h1 a half move ahead of white, and be up a pawn, but I doubt the Q+P vs Q ending is winnable given the position of the two kings.
A fascinating position! I am glad to say that my first instinct is, in fact, the correct one, but this is more due to the fact that the alternatives are just not palatable from a simple count.
So, let’s see why the alternatives are so bad:
1. h5 fg3!
This is the only move for black- he loses with any other-if black tries 1. …f3 loses to Kd3/d2 by white and the king reaches f1 in time to stop the pawn; and if black tries 1. …g4, white will still bring the king to the d-file to control the f-pawn, and white’s h-pawn can’t be stopped. Continuing:
2. h6
Doesn’t matter what white does here- with h6, he at least gets a queen on the board the half-move after black, but it is easy to see this won’t help since white’s king is on that deadly diagonal to h8 as I mentioned in my first comment:
2. …..g2 3. h7 g1Q 4. h8Q Qa1+ skewers and wins.
Alternatively, at move 1:
1. gf4 gh4!
Also, an only move for black- if black tries 1. …gf4?? white can push h5 to get his pawn far enough away from black’s king, and if black then tries f3, white has the tempi needed to stop the pawn. Continuing:
2. f5 Kc6!-+
Black draws only if he pushes the pawn since white queens the half-move after black. With white’s pawn on the f-file at f5, black has time to stop white’s pawn while white is helpless to stop the h-pawn. The rest is left as an exercise.
Alternatively, at move 1, white can try to move the king over, but this is also easily seen to be losing:
1. Kd3 fg3! (only move again) 2. Ke3
If 2.h5 or 2.hg5, black just pushes g2 to win easily. Continuing:
2. …..gh4-+ with a trivial win.
And, lastly, of course white can’t play 1.hg5 since 1. …fg3 and black will cover g8 with his queen a half-move before white can’t queen his.
This leaves the odd-looking 1.g4. I came to this move almost immediately since it was the only move that allows white to make a queen the half-move before black, but isn’t immediately killed with a skewer from a1. Black will be up a pawn in a queen ending, but without much in the way of winning chances:
1. g4! gh4!
Black should lose with 1. ..f3 since 2.Kd3 gets the white king close enough to stop both pawns and set himself up to win the resulting K+P vs K ending (though I will have to look at it later to be absolutely sure). Continuing:
2. g5!
There is no time to lose since black’s h-pawn is unstoppable. Continuing:
2. …..h3
I think black should queen the h-pawn here now since any winning chances will be minimized should he queen the f-pawn here and be forced to try to win with a rook’s pawn. Continuing:
3. g6 h2 4. g7 h1Q 5. g8Q
So, white has successfully gotten his queen on the board, but black has an extra pawn. Just based on the position of the kings and the pawn, I would think this is surely drawn and, so, I put it into the Nalimov tablebase, and it confirms this is a draw with best play. I also inputted the position that arises if black pushes the f-pawn at move 2, and it also drawn with best play.
1. g4 draws by a whisker. The point is that White can handle a Black f-pawn but not a g-pawn. If Black promotes the h-pawn, then White promotes her g-pawn just in time.
gxf and avoid queening on h8 due to a1h8 skewer?
The theory of the “square of the pawn” applies here, that is, the King would be able to catch up the pawn if in its next move, it enters the square bound by the following points: (1) square where the pawn is located; (2)the queening square; (3) the square in the 8th rank diagonally connecting to point 1; and (4) the square in the rank where the pawn is located that intersects 1 and 4.
Hence, the only move to draw would be 1. h5 as 1. hxg5 fails to 1…fxg3.
Kd3?
Kisses from Catalonia!
Kd3 or Kd2 also.
Kisses from Catalonia!
1. h5!
(1. gf? gh!
2. f5 Kc5
3. Kd3 h3
4. f6 Kd6
5. f7 Ke7
6. Ke3 h2
7. Kf2 h1Q -+)
(1. hg? fg!
2. g6 g2
3. g7 g1Q -+)
(1. Kd4? fg!
2. Ke3 gh! -+)
1… fg
2. h6 g2
3. h7 g1Q
4. h8Q =/+
Marcelo
A thought for Rosh-ha-Shanah: don’t think you have to take what’s on offer. L’Mehlak Tovah!
This comment has been removed by the author.
Oh, it says “White to play and draw”!
I broke my head trying to find a win 🙂
Any king move loses. Any pawn capture loses too. So by process of elimination, only g4 and h5 look feasible. h5 also loses due to Qa1+ and Qxh8. Hence the only realistic drawing chances are with g4. I would play:
1. g4
Just counting, and taking note of the fact that the white king is sitting on the a1/h8 diagonal, I think white has to play g4 here. If white passes on the first move with h5, black takes at g3 and queens the half move before white does at h8, and then skewers from a1 to win the new white queen. If white takes at g5 on the first move, black again queens at g1 a half move ahead and covers the g8 square. Finally, if white takes at f4 on the first move, black can take at h4 and black’s king can then play to c6/c5 to stop the white f-pawn. After 1. g4 gh4 2.g5, black can queen at h1 a half move ahead of white, and be up a pawn, but I doubt the Q+P vs Q ending is winnable given the position of the two kings.
1 Only g4 enables white to queen the pawn for a draw.
Most possibilities are easily excluded:
1. hxg5?? fxg3 must loose (Qg1 grabs Qg8)
1. h5? fxg3 gives Q vs. Q, black up with pawn.
1. g4? gxh4 the same.
So I can only find:
1. gxf4 gxh4
and hope this is a draw….
I decided to work it all out explicitly.
A fascinating position! I am glad to say that my first instinct is, in fact, the correct one, but this is more due to the fact that the alternatives are just not palatable from a simple count.
So, let’s see why the alternatives are so bad:
1. h5 fg3!
This is the only move for black- he loses with any other-if black tries 1. …f3 loses to Kd3/d2 by white and the king reaches f1 in time to stop the pawn; and if black tries 1. …g4, white will still bring the king to the d-file to control the f-pawn, and white’s h-pawn can’t be stopped. Continuing:
2. h6
Doesn’t matter what white does here- with h6, he at least gets a queen on the board the half-move after black, but it is easy to see this won’t help since white’s king is on that deadly diagonal to h8 as I mentioned in my first comment:
2. …..g2
3. h7 g1Q
4. h8Q Qa1+ skewers and wins.
Alternatively, at move 1:
1. gf4 gh4!
Also, an only move for black- if black tries 1. …gf4?? white can push h5 to get his pawn far enough away from black’s king, and if black then tries f3, white has the tempi needed to stop the pawn. Continuing:
2. f5 Kc6!-+
Black draws only if he pushes the pawn since white queens the half-move after black. With white’s pawn on the f-file at f5, black has time to stop white’s pawn while white is helpless to stop the h-pawn. The rest is left as an exercise.
Alternatively, at move 1, white can try to move the king over, but this is also easily seen to be losing:
1. Kd3 fg3! (only move again)
2. Ke3
If 2.h5 or 2.hg5, black just pushes g2 to win easily. Continuing:
2. …..gh4-+ with a trivial win.
And, lastly, of course white can’t play 1.hg5 since 1. …fg3 and black will cover g8 with his queen a half-move before white can’t queen his.
This leaves the odd-looking 1.g4. I came to this move almost immediately since it was the only move that allows white to make a queen the half-move before black, but isn’t immediately killed with a skewer from a1. Black will be up a pawn in a queen ending, but without much in the way of winning chances:
1. g4! gh4!
Black should lose with 1. ..f3 since 2.Kd3 gets the white king close enough to stop both pawns and set himself up to win the resulting K+P vs K ending (though I will have to look at it later to be absolutely sure). Continuing:
2. g5!
There is no time to lose since black’s h-pawn is unstoppable. Continuing:
2. …..h3
I think black should queen the h-pawn here now since any winning chances will be minimized should he queen the f-pawn here and be forced to try to win with a rook’s pawn. Continuing:
3. g6 h2
4. g7 h1Q
5. g8Q
So, white has successfully gotten his queen on the board, but black has an extra pawn. Just based on the position of the kings and the pawn, I would think this is surely drawn and, so, I put it into the Nalimov tablebase, and it confirms this is a draw with best play. I also inputted the position that arises if black pushes the f-pawn at move 2, and it also drawn with best play.
1. g4 draws by a whisker. The point is that White can handle a Black f-pawn but not a g-pawn. If Black promotes the h-pawn, then White promotes her g-pawn just in time.