White to mate in two.

Originally posted by schakuhr
your solution is wrong, and Mephisto has provided me with 4 wrong solutions so far.

what if black plays 2. ...fxg6 ?

I don't think you both are grasping the point of the puzzle completely.

What is wrong with my first solution (after 1.Rxf7+)
Clearly the first move must be a check or else Black forces perpetual check easily. The only two viable options are 1.Rxf7+ or 1.Rg8+). White needs the tempo to withdraw the Rook from a8 and if taken promote there a queen, or use it as a hiding place otherewise.
Now after 1.Rg8+ Kf6 2.Rg6+ if Black plays 2...fxg6 then 3.Rf8+ K~ 4.b8Q pretty much secures an endgame with White ending up with rook against Blacks' two split pawns. Since I have neither the time nor the patience to analyse it I'd assume it is a draw and the solution is 1.Rxf7+

Originally posted by fetofs
.---- .-.-.- -.- ..-. .....

Just adding up a bit:

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Originally posted by ilywrin
What is wrong with my first solution (after 1.Rxf7+)
Clearly the first move must be a check or else Black forces perpetual check easily. The only two viable options are 1.Rxf7+ or 1.Rg8+). White needs the tempo to withdraw the Rook from a8 and if taken promote there a queen, or use it as a hiding place otherewise.
Now after 1.Rg8+ Kf6 2.Rg6+ if Black plays ...[text shortened]... her the time nor the patience to analyse it I'd assume it is a draw and the solution is 1.Rxf7+

A) 1. Rxf7+? Kxf7 2. Rf8+ Ke7!
A1) 3. b8Q Rab2+ 4. Ka4 Ra2+ 5. Kb5 Rab2+ 6. Ka6 Ra2+ 7. Kb7 Rcb2+! 8. Ka8 (else draw by perpetual check) Rxb8+ and now white can't play axb8Q. 9. Rxb8 Kd7! is drawn.
A2) 3. a8Q Rab2+ 4. Ka4 Ra2+ 5. Kb5 Rab2+ 6. Ka6 Ra2+ 7. Kb6 Rab2+ 8. Ka7 Ra2+ and if white now plays 9. Kb8, black plays 9. ...Kxf8! game drawn.

B) 1. Rg8+! Kf6 2. Rg6+! fxg6 3. Rf8+ Ke7!
B1) 4. a8Q? - same thing as line A2, if the king takes shelter on b8, black plays Kxf8.
B2) 4. b8Q Rab2+ 5. Ka4 Ra2+ 6. Kb5 Rab2+ 7. Ka6 Ra2+ 8. Kb7 Rcb2+ 9. Ka8? Rxb8+ - the same as line A1.

Originally posted by schakuhr
A) 1. Rxf7+? Kxf7 2. Rf8+ Ke7!
A1) 3. b8Q Rab2+ 4. Ka4 Ra2+ 5. Kb5 Rab2+ 6. Ka6 Ra2+ 7. Kb7 Rcb2+! 8. Ka8 (else draw by perpetual check) Rxb8+ and now white can't play axb8Q. 9. Rxb8 Kd7! is drawn.
A2) 3. a8Q Rab2+ 4. Ka4 Ra2+ 5. Kb5 Rab2+ 6. Ka6 Ra2+ 7. Kb6 Rab2+ 8. Ka7 Ra2+ and if white now plays 9. Kb8, black plays 9. ...Kxf8! game drawn.

B) 1. Rg8 ...[text shortened]... b8Q Rab2+ 5. Ka4 Ra2+ 6. Kb5 Rab2+ 7. Ka6 Ra2+ 8. Kb7 Rcb2+ 9. Ka8? Rxb8+ - the same as line A1.

Thank you for the pointer, I had missed that. Only in B2) White needs to play:
9.Kc6 and seek shelter at g7 (behind Black's g-pawn) which in turn shows why 1.Rxf7+? fails. The line after 9.Kc6 is something like 9...Rc2+ 10.Kd5 Rd2+ 11.Ke4 Re2+ 12.Kf4! Rf2+ 13.Kg5 Rxf8 (or the kong makes it to g7) 14.Qb7+! and White wins one of the rooks.