Editor
You have black bailing out into a materially lost position by playing this line: 1.a8(R) Rb3 2.b8(R) Rd3 3.d8(R) Rxd1. Black can keep forcing white to find more difficult lines by continuing across the 3rd rank. Black could have even played 2. ....Rc3 instead of jumping to the d-file. The main line is 1.a8(R) Rb3 2.b8(R) Rc3 3.c8(R)......etc. until the black rook reaches the f-file.
Yancey, I don't understand what move do you have in mind?
Editor
Alena, you have main idea, but not the main line. Black doesn't need to cooperate with 3. ....Rxd1. Black doesn't even need to skip the c3 square with the rook at move 2 either.
1.a8=R Rb3
2.b8=R Rd3
3.d8=R Rxd1
4.R1Xb2 Nf2+
5.Rxf2 g2
6.Ra3 Ra1
7.Rad3 Kh1
8.Rxg2 Rxg2
9.f8=Q Rh2+
10.Kg4 Ra4+
11.R8d4 Ra1
12.e8=Q Rg2+
13.Kh5 Ra5+
14.Rd5 Rxd5+
15.Rxd5 Ng3+
16.Kh6 Kh2
17.Qf4 Ra2
18.Qg8 Ra6+
19.Rd6 Ra3
20.Rd2+ Kh1
21.Qd5+ Rf3
22.Rd1+ Kh2
23.Qxg3+ Kxg3
24.Rg8+ Kh2
25.Qe5+ Rf4
26.Qxf4+ Kh3
27.Qg3#
Sir , where do you find these amazing puzzles
