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Is it Bh3! After Bh3 I don’t see a way for black to stop Qg8!
1. Rxe6+!
The only thing I can think of is: Lh6, with the idea of taking rock on c8 after Dg8+.
I have to admit this is a very difficult problem. 🙂
I actually remember this problem well even 3 years later. My solution was R6d4 (but I overlooked the best continuation in even that line), but other commenters suggested Bh6 which looks good in some lines, but I could never find a line that seemed clearly better than the R6d4 line. Let’s take another look at both lines:
1. R6d4 Qe5 (eyeing g7 and h8)
If white tries a move like Qg2, he loses quickly to Rh4. More testing is Qe2 attacking the rook at d1, but then white can leave the rooks doubled and attack with Bh6 and gain a similar advantage. Continuing:
2. Bh6
I went wrong here the last time. I thought 2.Rh4 was good, but 2. …Qg7 provided adequate defense since the black queen gets back and by attacking the white queen forecloses on the option of Bh6. Continuing:
2. …..Qf6
No better move here for black, I think. White is threatening Qg8+ winning the rook at c8. Black could move the king to e7, but white can stir up the attack: [2. …Ke7 3.Bf4! Qg7 4.Bg5! Ke8 5.Qe6! Re7 (or 5. …de6?? 6.Rd8 Rd8 7.Rd8#; or 5. …Kf8 6.Qd6 Kg8 7.Rg1 Re8 8.Rb4) 6.Qe7 Qe7 7.Be7 winning the exchange]; or [2. …Qh8 3.Rd6! Bd5 4.R6d5! Qh7 (or 4. …ed5?? 5.Re1+-) 5.Qg5 f4 6.R5d3 wins a piece]. Continuing from move 2 above:
3. Qg8 Ke7
Here, Rf8 is going to be worse after 4.Bf8 Qf8 5.Qh7 and Rg1-Rg8 is coming. Continuing:
4. Qc8 Qh6 wins the exchange.
In the above line, white still gets Bh6 in in time, but there is no reason to wait for a move to do so:
1. Bh6!
As before, it threatens Qg8 winning the rook at c8. Ke7 is no defense since white just checks from g5 first: [1. …Ke7? 2.Qg5 Rf6 (or get mated) 3.Bg7 wins a full rook since 3. …Qe5 4.Bf6 Qf6 5.Rd7 Bd7 6.Rd7 Kd7 7.Qf6 is just as bad]. Best for black is to defend g8 with the queen from g4. Continuing:
1. …..Qg4
2. Re6!
Not possible on the first move due to the queen at e4. Now that she has been diverted to deal with another threat, this move is a good one. Continuing:
2. …..de6
Here, Kd8 loses: [Kd8 3.Bg5 Kc7 4.Rc6! dc6 5.Qf7+-]. Continuing:
3. Qe6 Re7 (only move)
4. Qc8 Kf7
5. Qf8!
Remember, the black queen is attacking the rook at d1 here. Easy to overlook that. Continuing:
5. …..Ke6
Or [5. …Kg6? 6.Rd6! Kh5 (or 6….Kh7 7.Qe7 Kh8 8.Rd8+-) 7.Qe7 Qg1 8.Bc1+-]. Continuing:
6. Qd8
I spent a long time looking at this position 3 year ago, and just a bit tonight, and I don’t see a better continuation, here, or at move 5 above for white. He is clearly ahead due to black’s exposed king. But knocking white out doesn’t seem so trivial to me. Perhaps a new group of commenters can shed more light on this.
Bh6
Hard to find.
difficult.
may be Bh6, with the idea Dg8+ and then take the rook on c8.
R6d4 Qe5; Rh4 Kf7; Bf6! Rxf6; Rh8+ Ke7; Qg7+ Rf7; Qxe5 wins the Queen for a Bishop.
John Holliday