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1. Qb1!!
Keeps e4 protected, restricts moves by black king, and it threats Qb5+ Kd4 Qd5#, the only mate threat I can find in this diagram. Black has no check, and I see no good moves against the mate threat. Black probably ends up loosing his queen to a pin.
1. … Kd4 (Qg8? Qa2+)
2. Qb3!
Again threats Qd5#, again black has no Qg8 against it, so enforced is:
2. … Kxe4
3. Qb1+
At first I saw no mate threat here and thought black king would end up happy in a-file after e.g Qf3.
I was about to give up when I thougt: “must make black eat that e-pawn”. Seemed unlikely at first, but Q in b-file, on white fields, actually seems to make it happen?
When you’re down material in a queen ending, look for mate threats. If none are available, look for checks.
Fortunately for white, Black’s K is in a very precarious position.
1. Qb1 threatens 2. Qb5+ and 3. Qd5#. Black’s only defense is 1…Kd4. Now 2. Qb3 threatens 3. Qd5#. (What a monster the pd2 is!!) Even 2…Q:e4+ doesn’t help, 3. Kd6 leaves Black with no good checks.
3…Qd3 offering to trade Queens allows 4. Qd4# (I bet you’ve never seen this mating position before!) so black must move the Q while continuing to defend the mate threat on d5. This means the Q must stay on the a8-h1 diagonal. b7, c6, d5, and f3 all lose the Q immediately (and d5 with mate). Leaving the Q on e4 and pushing the h-pawn allows 4. Qc3# Moving the Q to g2 or h1 allows 4. Qc3+ and 5. Qc6+ winning the Black Q. So Black must play 3…Qa8.
However, this should allow White to pretty easily force winning positions such as White Qb5 Kc7 and Black Qa8 Ka7 with Black to move but having no good option. 4. Qe3+ looks like a good start, Black must play 4…Kc4 when 5. Qc3+ forces …Kb5. I think the rest is easy.
Absolutely an incredible study, well worth the insomnia (I’m typing this at 4 AM). Who composed it? It’s a wonderful demonstration of just how effectively an active Queen can dominate a passive one, all with the help of one teeny tiny pawn on d2.
This is one of H. Rinck classics from 1906!
A beautiful example of Queen domination.
1. Qb1! (1. Qf3? Kb4) Kd4
2. Qb3 Qxe4+
3. Kd6 Qa8 (if Qg2/h1 3. Qc3+ followed by the skewer 4. Qc6+)
4. Qe3+ Kc4
5. Qc3+ Kb5
6. Qb3+ Ka6
7. Qa4+ Kb7
8. Qb5+ Ka7
9. Kc7 and white mates quickly.
1. Qb1 Kd4(Threat: 2.Qb5+ Kd4 3. Qd5#)
2. Qb3!! Qxe4+
3. Kd6 Qa8 (Threat: 4.Qc3#, If 4…Qg2/h1 4. Qc3+ Ke4 5. Qc6+ wins the queen by skewer)
4. Qe3+ Kc4 5. Qc3+ Kb5
6. Qb3+ Ka6 (Or 6…Ka5 7. Qa3/a2+7 winning the queen by skewer again)
7. Qa4+ Kb7 8. Qb5+ Ka7 (8…Kc8 9. Qd7+ Kb8 10. Qd7#)
9. Kc7! and 10. Qb6# is unstoppable).
1.Qb1
1.Qb1
<1.Qb1>
1.Qb1
My instinct tells me it has to be Qb1 simply to keep the king corralled and from escaping through d3 while, at the same time, protecting e4:
1. Qb1
Threatens 2.Qb5 followed by 3.Qd5#. Black cannot protect d5 with the queen without allowing the skewer from a2, so I think the black king has to move on the first move, and there is only Kd4:
1. …..Kd4
Now, what for white? Susan didn’t state that it was “white to move and win”, but I don’t think this would be a chess problem if it weren’t the case that white wins. After the first moves, black is now threatening Qxe4 forcing the exchange of queens for a winning endgame. It is tempting to move the king to d6 so that white can reply to Qxe4 with Qb3:
2. Kd6? Qe4??
3. Qb3!
And white has the deadly threat of Qc3# that black can only parry with Qd3, but then white mates with Qd5 instead. Finally, black can open a hole for the king by moving the queen along the long diagonal (keeping an eye on d5, but this allows white to win the queen or enforce mate: [3. …Qg2/h1 4.Qc3 Ke4 5.Qc6+- wins the queen]; or, a bit more complicated, but otherwise straightforward [3. …Qa8 4.Qe3+! Kc4 5.Qc3+ Kb5 6.Qb3+ Ka6 7.Qa4+ Kb7 8.Qb5! Ka7 (or 8. …Kc8 9.Qd7! Kb8 10.Qc7#) 9.Kc7!! and the mate is unavoidable]. However, black need not cooperate by taking at e4 on move 2:
2. …..Qh6! (Qf7 ok too, I think)
And now I don’t see how black can be prevented from extracting the king. Black is threating f5 with discovered check, and a likely win as white will find it difficult at best to avoid the forced exchange of queens. Also, black is threatening the d2 pawn with similar consequences. The only check that doesn’t drop the e-pawn immediately is Qb4, and a plausible line might continue:
3. Qb4 Kd3
4. Qc3 Ke2
5. Qc4 Kd2
6. Kd5 Qe3 and only black can win this (I don’t know for sure it is won for black, but I would guess it is).
So, at move 2, can white profitably play Qb3 first? I think white can. Let’s take it from the top:
1. Qb1 Kd4
2. Qb3
Obviously, white’s threats are Qc3+ and Qd5# if black moves a pawn. The black king can only move to capture at e4, but then loses the queen to 3.Qc2+. And black cannot guard the d5 square from anywhere safe. This leaves only the queen capture at e4, but we already know the problem this presents to black:
2. …..Qe4+
3. Kd6!
And we have reached the position discussed above where black faces either losing his queen by playing 3. …Qg2/h1, or getting mated if he tries Qa8.
So, I think white wins with 1.Qb3
Qb1