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Give up. No one can hold da a pawn.
White has to give up. The a pawn can not be stoped.
I guess a draw.
1. e5! a3 (Qxe5?? Qg7+ Ke8 f7+ wins)
2. e6! Qa8+ (a2?? a7+ wins. Qxd7?? Kxd7 wins)
3. Kd6 Qb8+
4. Qc7 Qxc7
5. Kxc7 a2
6. Kd7 a1=Q
7. e7+ Kg8
8. e8=Q+ Kh7
is a complicated situation….
Pretty problem. Been a while I’ve posted here, so feels good to be back with a good problem too.
Left to himself, black would want to exchange queens at d7 and then promote his a-pawn. Trying to get out of the pin is clearly wasted effort for white. So the first move for white is clear enough: 1. e5.
Having analyzed this move now, I will upgrade it to: 1. e5!!
Black has 3 viable responses. Let us see all of them.
1… Qxd7+
2. Kxd7 and now the e-pawn cannot be stopped from promoting, also it can easily stop black’s a-pawn (since it gains two tempos via checks).
1… Qf7
2. Qd6+ Kg8
3. e6 Qxf6
4. e7 Qxd6+
5. Kxd6 Kf7
6. Kd7 and white promotes first and prevents black from doing so.
1… a3
2. e6 a2
3. Kc7! (now white threatens an immediate 4. Qg7#)
3… Qxd7+
4. Kxd7 a1Q
5. e7+ Kf7 (5… Kg8? 6. e8Q+ Kh7 7. Qh5+ Kg8 8. Qg6+ and mate next move)
6. e8Q+ Kxf6
7. Qh8+ and black’s newly minted queen is lost.
does Kd6 fail because of .. Qb8+ ? Or how exactly?
My first instinct was Kd6 then force queens to trade on E7 but I’m honestly not very good.
pht’s e5 move seems very good. I’ll even give it two exclamation marks! White should not draw or resign.
[FEN “4qk2/3Q4/1pK2P2/2p5/p1P1P3/8/8/8 w – – 0 0”]
{pht’s variation:}
1. e5!! a3
2. e6 Qa8+
3. Kd6 Qb8+
4. Qc7 Qxc7+
5. Kxc7 a2
6. Kd7 a1=Q
7. e7+ Kg8
8. e8=Q+ Kh7
{Continuing pht’s variation, mate follows quickly}
9. Qh5+ Kg8
10. Qg6+ Kh8
11. Qg7#
{But what if white responds Qxd7+ rather than a3?}
1… Qxd7+
2. Kxd7 Kf7 {Black cannot stop white’s e-file pawn.}
3. e6+ Kxf6
4. e7 Ke5
5. e8=Q+ Kd4 {The black king escapes a quick mate, but not for long.}
6. Qe2 Kc3
7. Qa2 Kb4
8. Kc6 a3
9. Kd5 b5?
10. cxb5 c4
11. Qxc4+ Ka5
12. Kc5 a2
13. Qb4#
{Fritz 13 would have played it like this:}
1…Qf7
2. Qxf7+ Kxf7
3. Kd6 Kg6
4. e6 Kxf6
5. e7 a3
6. e8=Q Kg5
7. Qe3+ Kf5
8. Kd7 b5
9. Qxc5+ Kg6
10. cxb5 a2
11. Qc2+ Kg5
12. Qxa2 Kf5
13. b6 Ke5
14. b7 Ke4
15. Qe6+ Kf4
16. b8=Q+ Kf3
17. Qf8+ Kg3
18. Qeg8+ Kh4
19. Qh6#
Kc7!! 1-0
After 1.e5 a3 2.e6 Qa8+ 3.Kd6 Qb8+ I would prefer 4.Kd5 Qa8+ 5.Ke5 Qb8+ 6.Kf5 when black has no good move left. Of course 6.Qd6+ exchanging Qs also wins.
On the other hand 1.e5 a3 2.e6 If now 2…. a2 3.Kc7!! this threatens mate at f7 by Q. Q exchange does not help as shown by many comments above. Plausible move at first sight 3… Qg6 fails 4.e7+ Kg8 5.e8=Q+ Qxe8 6.Qg7#
A good problem on the issue of time, and how some pawn moves gain time via checking- something to always have in the back of your mind in pawn endings where the king is trying to hinder the advances.