I will just say that like most modern puzzles, getting the position down to a winning position that can be verified by the tablebases is all the puzzle composer requires for a solution. The solution Krug gives ends basically at move 9 in Umeshn's line, but of course with 1. c8N as the start.

I would say that for me, I would have an easier time winning Q+N+P vs R+B+N than the ending Alena finds Q+P vs B+N. The addition of a knight to the queen is quite a bit more power than trading that knight for the black rook- the queen is major power enhancer to any piece and vice versa.

Q+N+P against R+N+B ending!

Now, 1. c8=N will prevent 1... Ra7+, and 1... Rxc8 will proceed as above. But Does Black have much choice? How can he prevent 2. g8=Q?

Wow, 1. c8=Q Ra7+ draws!

Alena, though you don't have the main line after 1. ....Ra1, it is one of the main variations. As for how to win after black's 9th move, I could not really tell you without a lot work or referring to the Nalimov, but I would imagine the most direct plan will be to force the black king down towards the pawn by using attacks and checks with the queen while bringing the white king at least to f6 at some point- once the black king is forced to g3 allowing a check from h3 or f3 with the queen, it is probable that black will be in some sort of zugzwang that loses one of the pieces. I can sort of see what some of those positions might be, but the details would take some work. The sort of position I have in mind would be something like this to work toward: 8/8/5K2/8/5b1n/6kQ/6P1/8 b - - 0 1

Umeshpn, you have a lot of that correct except for the very start. Both you and Alena could learn a lot from each other's line.

s position makes a difference: 9. g4+ Kh4 (9... Kh6 10. g8=Q and Black doesn't have 10... Nh6+) 10. g5!, and now since the BN cannot go to h6, White queens.

1. c8=Q Rxc8 2. Kxc8 Nd6+ 3. Kd7 Ne4 4. Ke6 Ng5 5. Ke7 (5. Kf6? Be5+? 6. Kxe5 Nf7+ followed by 7... Nh6 =) Bd6+ 6. Kd7 (6. Kxd6 Nf7+ and 7... Nh6) Ne4

Now we have reached the same position after the third move, except that the Black Bishop is on d6 instead of g3, and that makes a real difference!

1. Ke6 Ng5+ 8. Kf5! Nf7

Now the Bishop'

At first I promoted to a queen and thought that I solved the puzzle. The varition was 1.c8=Q Rxc8. But when I began to work out the second varition 1.c8=Q Ra7+ I understood that I didn't solve it.
Then I guessed that I need to block the black rook. It could be done with the help of the knight.

1.c8=N Ra1
2.g8=Q Rd1+
3.Ke7 Nd4
4.Qd5+ Kg6
5.Ke8 Re1+
6.Ne7+ Rxe7+
7.Kxe7 Nf5+
8.Ke6 Ng7+
9.Kd7 Nf5
I know that it's a theoretical win but I don't have enough skills to actually win it.