THIS IS FORCED # IN 10 WITH MULTIPLE VARIATIONS THIS SITE IS USED TO SUBMIT A LOT OF PUZZLES OF THIS TYPE WHICH IS DIFFICULT TO FOLLOW ANSWERS IN TEXT. IT WILL BE MORE CONVINIENT IF THERE IS PGN PROGRAMMING.

1.Rg4+ Kh8 2.Qe3 Kh7 3.Rh4 Kg6 4.Rxh6+ Kg7 IF 4... Kf5 5. Rh5+ Ke6 6. exf6+ Kd7 AND IF 6... Kxf6 7. Qh6# OR IF 6... Kd6 7.Qxe7+ Kc6 8. b5# 7.Qxe7+ Kc8 8.Rc5+ Kb8 9.Qxf8+ Nc8 10.Qxc8# 5.Rh5 Qc5 SURVIVING MORE
IF 5... Rh8 6. Qg3+ Kf8 7. Rxh8# 6.bxc5 Rh8 7.exf6+ Kxf6 IF 7... Kg8 8. Qe8# OR IF 7... Kf8 8. Rxh8# 8.Qe5+ Kg6 9.Qg5#

1. Rg4+ Kh8, 2. Qe3! Kh7, 3. Rh4! Kg6, 4. Rxh6+ Kf5, 5. Rh5+!

a) 5...Kg6, 6. Qh6#

b) 5...Kg4, 6. Qf3#

c) 5...Ke6, 6. exf6+! (discovered check) Kxf6, 7. Qh6#

d) 5...Ke6, 6. exf6+! Kd7, 7. Qxe7+ Kc8, 8. Rc5+ Kb8, 9. Qxf8+ Nc8, 10. Qxc8#

1. Rg4+ Kh8, 2. Qe3! Kh7, 3. Rh4! Kg6, 4. Rxh6+ Kg7, 5. Rh5! Rh8, 6. Qg3+ Kf8, 7. Rxh8#

So, I went an looked up the game- I was right- it is a forced mate in 10, but Shtembuliak diverted to a Q vs R+N ending rather than keeping the black king in the mating net- in the line I gave it continued 4....Kg7 5.exf6+? allowing black to give up the queen for the rook to escape mate. White should have played 5.Rh5/4/3 to make room for the white queen on h6- this forces black to start sacrificial delays like 5....Qc5 etc.

I never noticed the edit function until just now!

I think it probably a forced mate after 1.Rg4+ Kh8 2.Qe3 Kh7 3.Rh4 Kg6 4.Rxh6+. Hard to believe the black king can escape mate after this.