From The Saavedra Problem: Amazing Endgame Tactics

Aloha!  Today we are going to look at a puzzle called the Saavedra Position.  Saavedra was a Spanish priest who lived in the 1800s, and who found some cruel and unusual tactics in an endgame.  The original Saavedra position starts here.  Click through the moves to learn what to do if this happens to you!  By, Mrs Jessica E Prescott (aka BoundingOwl).

What's the threat?  The king wants to eat the rook, and also promote the pawn!  Is there anyway black can stop both threats?  Yes!  Black can try for a stalemate to save the day.  What would happen if white promotes to a queen after Rd4? 
Can you find a way for black to force a stalemate?  This move is also a fork!  If white doesn't take, black will win a king and rook endgame!
Great!  Okay, but white doesn't have to promote to a queen...does she?  What else could she become?
That's right!  And as a rook, you still get to threaten checkmate!  Black's Rc4 trick doesn't work anymore, because it would not be stalemate if white captured.  White would just say THANKS and bu-bye!  Kiss
Black can stop white's checkmate threat.  (Do you see the mate on a8?)  But not for long!  If black plays Ra4 to try to protect the a file, white has a super sneaky king move that wins the game.  Can you find it?
Fantastic effort you guys!  This puzzle is really neat because I think many people would just automatically call it a draw.  But always try to look for tricks!  Click on all the links for more practice and cruel and unusual words!