You're of course correct with the first move, but easier is
1. Rxf7+! Kxf7 2. Qh7+ Kf6 3. Qxh6+! Kf7 4. Rf1+ Kg8 5. Qg6+ Kh8 6. Rf7 Qxg4+ [ 6. ...Qxd4+ 7. exd4 same result ]
7. hxg4 Rxd4 (or whatever)
8. Rh7# ...wasn't the task to mate in 9
After 3. Rf1+ Kg5
[ 3. ...Ke6 leads to mate faster 4. Qe4+ Kd6 5. Qe5+ Kc6 6. Qc5# ;
also noteworthy is 3...Qf5 4. Qxh6+ [ not 4. Qxf5+ ] Kf7 5. Rxf5+ Kg8 6. Qg6+ Kh8 7. Rh5# ]
4. Rf5+ Qxf5
[ 4. ...Kh4 5. Qxh6+ Kg3 6. Qe3+ Kh4 7. Rh5# ]
5. Qxf5+ Kh4 6. Kg2 Rd5 7. Qxd5 e5 8. Qf7 Kg5 9. Qf5+ Kh4 10. Qh5# you "only" have mate in 10
Subject: puzzle 4 
Thu 23 Feb - 9:35
