Rxe4 looks like black loses a piece. The recapture d5xe4 allows Qd8+ which wins black’s queen and may lead to mate anyway (no tie to explore further–cheers!)
Like the anonymous commenter at 4:06PM CDT, my eye falls on Rxe4 as the start, but I now think this is wrong:
1. Re4? de4?! (ab2 is below) 2. Qd8?
Not the best move for white, but is, in fact, why 1.Re4 looks so enticing at first- white plans a skewer on the king and queen after black plays 2. …Kf7, but, unfortunately….
2. …..Rf8!
And now what for white? If, at move two, white takes at a3, he might find a way to hold, but I doubt it. He has no winning chances that I can see.
Finally, at move 1, I did consider briefly Rxd5, but this will lose since the discovered pin is deadly:
This was a tougher tactical problem than most posted here, at least for me. I mostly stumbled onto the right idea through trial and error, but there are multiple lines one has to consider here, and I am not going to show them all, but just the flavors to highlight the idea:
1. Rb4!
The idea is to deflect the black queen from her coverage of the back rank and the d5 pawn. Let’s first see why black cannot take the rook:
1. …..Qb4? 2. Qd5! Re6
Nothing better: [2. …Kh8 3.Rc8 Qf8 (or 3. …Rf8 4.Qf7+-) 4.Qd7 with two mating threats that can’t both be stopped]; or [2. …Kf8 3.Qd8 Kf7 4.Rc7 with either 5.Qd7 or 5.Re7# on the next move]; or [2. …Rf7 3.Rc8 Qf8 4.Rf8 Kf8 5.Qd8#]. Continuing from 2. …Re6 above:
3. Qe6 Rf7
Of course, Kf8 is mate after 3.Rc8. No better is 3. …Kh8 4.Qf5! with unstoppable mating threats of Rc8, Qf8 etc. Continuing:
4. Rc8 Qf8 5. Rf8 Kf8 6. Qc8 Ke7 7. ba3 with a decisive material edge, and probably a forced mate in here somewhere.
So, black has to find a different defense at move 1. Let’s walk through the alternatives:
1. Rb4 Qd7 (keeping guard on d5) 2. Qb3
Not sure what is best here for white, but pretty sure this wins. Continuing:
2. …..ab2 (alternatives below) 3. Rb8 Kf7 (Rf8 4.Rf8 Kf8 5.Qb8) 4. Rb7 bc1(Q) 5. Rd7 Ke8 6. Bc1 Nc5 (Kd7 7.Qb7+-) 7. Qd5 Nd7 8. g4 Rf8 9. e6 and this is easily won for white now.
At move 2 in the line above, black does no better with Rf8, but it takes work to show this:
And white is going to double the rooks on the 7th rank if black takes at h6 or b2, and the game will reduce down to a Q+B vs R+R ending where white has a decisive material edge. The only different continuation I can see is to play 8. …a2 instead, and this so complicated, I don’t even know for sure if it doesn’t hold for black. I don’t think it does- here is a plausible line I worked through that looks most forced to me, and looks decisive for white:
Like I wrote above- complicated. I am probably missing quicker, more decisive lines for white- like, for example 6.Rh7, but I am too tired to work it all out on that line.
1.Rb4!
If 1…Qxb4
2.Qxd5+ and the position is very complicated for black.
1. Rb4
if
1… Qxb4
2. Qxd5+ Kf8
3. Rc8+ Ke7
4. Rc7+
1-0
if
1. … Qa8 (guarding c8 and d5)
2. Qxb3 Rf8
3. Rb7
now if 3… Ra5 4. R1c7 wins
or if 3… a2
4. Qxd5+ Kh8
5. Qd7 wins
Rxe4 looks like black loses a piece. The recapture d5xe4 allows Qd8+ which wins black’s queen and may lead to mate anyway (no tie to explore further–cheers!)
1. Rb4!
A.
1. Qxb4
2. Qxd5+ Rf7
3. Rc8+ Qf8
4. Rxf8+ Kxf8
5. Qd8#
B.
1. Qa8
2. Qxb3 Rf8
3. Rb7 Ra5
4. bxa3
Like the anonymous commenter at 4:06PM CDT, my eye falls on Rxe4 as the start, but I now think this is wrong:
1. Re4? de4?! (ab2 is below)
2. Qd8?
Not the best move for white, but is, in fact, why 1.Re4 looks so enticing at first- white plans a skewer on the king and queen after black plays 2. …Kf7, but, unfortunately….
2. …..Rf8!
And now what for white? If, at move two, white takes at a3, he might find a way to hold, but I doubt it. He has no winning chances that I can see.
Finally, at move 1, I did consider briefly Rxd5, but this will lose since the discovered pin is deadly:
1. Rd5?? Nf6! (pins the rook)
2. ef6 Qd5+
3. Qd5 Rd5
4. ba3 b2!
5. Rb1 Ra3
6. Kf2 Rdd3
And white is going to lose the bishop, or black is going to win the rook for the pawn- white can choose his fatal dose of poison.
In my next comment, I will discuss a more promising plan for white.
This was a tougher tactical problem than most posted here, at least for me. I mostly stumbled onto the right idea through trial and error, but there are multiple lines one has to consider here, and I am not going to show them all, but just the flavors to highlight the idea:
1. Rb4!
The idea is to deflect the black queen from her coverage of the back rank and the d5 pawn. Let’s first see why black cannot take the rook:
1. …..Qb4?
2. Qd5! Re6
Nothing better: [2. …Kh8 3.Rc8 Qf8 (or 3. …Rf8 4.Qf7+-) 4.Qd7 with two mating threats that can’t both be stopped]; or [2. …Kf8 3.Qd8 Kf7 4.Rc7 with either 5.Qd7 or 5.Re7# on the next move]; or [2. …Rf7 3.Rc8 Qf8 4.Rf8 Kf8 5.Qd8#]. Continuing from 2. …Re6 above:
3. Qe6 Rf7
Of course, Kf8 is mate after 3.Rc8. No better is 3. …Kh8 4.Qf5! with unstoppable mating threats of Rc8, Qf8 etc. Continuing:
4. Rc8 Qf8
5. Rf8 Kf8
6. Qc8 Ke7
7. ba3 with a decisive material edge, and probably a forced mate in here somewhere.
So, black has to find a different defense at move 1. Let’s walk through the alternatives:
1. Rb4 Qd7 (keeping guard on d5)
2. Qb3
Not sure what is best here for white, but pretty sure this wins. Continuing:
2. …..ab2 (alternatives below)
3. Rb8 Kf7 (Rf8 4.Rf8 Kf8 5.Qb8)
4. Rb7 bc1(Q)
5. Rd7 Ke8
6. Bc1 Nc5 (Kd7 7.Qb7+-)
7. Qd5 Nd7
8. g4 Rf8
9. e6 and this is easily won for white now.
At move 2 in the line above, black does no better with Rf8, but it takes work to show this:
2. …..Rf8
3. Rb7! Qg4 (what else?)
4. Qd5 Re6
5. Rg7 Kh8
6. Qe4
I think white can win with 6.Rxh7, but am not as confident in that line with the limited work I have done on it. Continuing:
6. …..Qe2
Or [6. …ab2 7.Rcc7 Qe2 8.Kh1! Qh5 9.Kg1! Qd1 10.Kf2+-]. Continuing:
7. Kh1! Qh5
8. Kg1!
And white is going to double the rooks on the 7th rank if black takes at h6 or b2, and the game will reduce down to a Q+B vs R+R ending where white has a decisive material edge. The only different continuation I can see is to play 8. …a2 instead, and this so complicated, I don’t even know for sure if it doesn’t hold for black. I don’t think it does- here is a plausible line I worked through that looks most forced to me, and looks decisive for white:
8. …..a2
9. Rf7 Rfe8 (what better?)
10.Qb7 Qh6 (forced)
11.Ra1 Qh3 (what else?)
12.Bf2 g5 (again, what else?)
13.Ra2 Rh6 (again, what else?)
14.Ra7 Qh2
15.Kf1 Qh3 (what else?)
16.Ke2 Qh5 (what else?)
17.Ke3 gf4
18.gf4 Qh3
19.Kd2 Rd8
20.Rd7 Qd7
21.Qd7 Rd7
22.Rd7 with a decisive edge.
Like I wrote above- complicated. I am probably missing quicker, more decisive lines for white- like, for example 6.Rh7, but I am too tired to work it all out on that line.