Here is a puzzle, split in three depending on black's second move. Some explaination in the 'move list'. Check it out:

In the first one, promote to queen and don't take the rook when it checks (Kh2).

thanks for the feedback, but we have Kh2 Rh1+ Kxh1

Ah yes, silly me.  I dashed off that response too quickly.  Nice case of under promotion.

I don't get it.  What happens next?

In all three problems, white underpromotes, then takes black's queen- what now?

 Well, the 2nd and 3rd variations are easily won for White. The lone Black rook (without any passed pawns to mount an attack of its own with),  doesn't stand a chance against a rook and knight, or even just two knights, as it will be unable to defend its helpless pawn against a double-attack. Once White captures the pawn, it will be easy enough to force his lead pawn through to promotion, using one piece to defend the pawn and the other to control the square directly in front of it.

   Now, the first variation is a whole different matter. The light-square bishop's inability to attack Black's remaining pawn will make capturing it very difficult, indeed. White will need to rush his king over to f5 before Black's king can get close, which may, in fact, be impossible.

 im awfully sorry, but im sort of new and i didnt fully understand your answer, would you mind elaborating for me?

Frantisek Prokop 1927

For problem 1 why not promote to queen? It has the same movements and more than a bishop. And white would have to keep forcing check or finally take the black queen because you have Qd1+ Kh2 Rf6#

Thanks Heinzie, I lost the details.

LiveAndLearn & uprising53, black can force stalemate Bb8+ Kxb8 c7+ Kb7 c=Q+ Ka7 Nxd5 (forced) Rf1+ Kh2 Rh1+ Kxh1 stalemate.

cobra91, you are right the first diagram is very complex, I'm not sure what are the main continuations here. There may be the opportunity of trading the Knight for the black pawn and running the king up.

Yes I used my chess google skillz for that one :p

wow ok thanks! thats actually sick

 Trading off the knight for the pawn is no good...Black will then station his king on g7, leaving White with zero winning chances.

I have to admit, now I'm actually curious as to how White would proceed to win the endgame that follows 1.Bb8+ Kxb8  2.c7+ Kb7  3.c8=B+ Kb8  4.Nxd5 Rd6  5.Ne7 Kc7.  Perhaps Bf5 would help by forcing the rook to defend from either g7 or g8. Maybe the knight could then take g7 away from the rook by attacking the pawn from e6, leading to some interesting opposition/zugzwang possibilities ...

Yeah, I don't really have enough experience to be acting as though I understand endgames- this is a matter for much stronger chess players to sort out!

shrug...this is how chessmaster did it against himself. 

Hey damon what's up mate I'm back in the state. If ya haven't got too many exams we should have beers this weekend

thanks for this problem