Solution.

Congrats to @heimindanger for solving this chess riddle and thus being the winner of this round! :)

Here now the full solution of the problem:

1. Nxe6+! dxe6
2. d7

And now:

a)

2. ... Bxd7
3. Rxd7 Ne7
4. Rxa5! ...

a1)

4. ... Rc8 (That's how the game continued.)
4. Rxe7! Kxe7 (In case of 4. ... Qxe7 white had won with 5. Ba3 b4!? 6. Bxb4 Qxb4!? 7. Ra7!)
5. Ba3 (And white won.)

End position:

https://cdn.steemitimages.com/DQmNhtzDot19NUbHTu6Lt5Yaa6f6nKM22g8ySFmVypvoCzZ/Chess_problem73_L-a1.jpg

a2)

4. ... Qc8! (This move had been the best black try.)
5. Ba3! b4! (5. ... Rxa5 6. Rxe7; 5. ... Qxd7 6. Rxa8+)
6. Rxe7! (6. Bxb4? Rxa5!, threatens check at a1.) 6. ... Kxe7
7. Bxb4+ Kd7
8. Qf7+ Kc6
9. Rc5+ Kb6
10. f3! (And in the long run white should win because black won't find a save place for his king.)

End position:

https://cdn.steemitimages.com/DQme8RcUxYXj8nJfCtxXne4rqrPquNxs3FcKKae3u3VmMjz/Chess_problem73_L-a2.jpg

b)

2. ... Ke7!?
3. dxc8N+ Rhxc8
4. g4 Rd8
5. Re1 (5. Rxd8? Rxd8 6. gxf5 Rd1+ 7. Kg2 Qd5+ results in a draw.) 5. ... Qe5!?
6. Kf1 (6. Rxe5? Rd1+ 7. Kg2 Nh4+ and black wins.) 6. ... Qxh2
7. gxf5 Qh1+
8. Qg1 (And white has the better position.)

End position:

https://cdn.steemitimages.com/DQmRYvokBrMNP76mFCHthWMKXgxgdNGU8ECFbeiRotkVFuh/Chess_problem73_L-b.jpg