WHITE TO PLAY AND DRAW.
SOLUTION: Black pawn duo are too much for white bishop duo! Hence white must use tricks to draw this position. When you see the position of white king, the first thing that must strike your mind is the possibility of stalemate. now if black were to play gh2 then white will get to move his g3 pawn and then stalemate possibilities wont remain. Hence the first and the most obvious move has to be 1.Bg1
Now time for some calculation. If 1...Kb1 then 2.Bd4 a2 3.Bb2 Kb2 and its a stalemate! So the Bishop on b1 cannot be taken. That leaves us with only 1 move. 1...a2
Now the threat is ab1=Q and hence we will have to move the B. Lets choose a random square say 2.Be4 now 2...b1=Q 3.Bd4 Qb2 and if now queen is taken then the 'a' pawn will queen and white will not be stalemated because he will be left with a B on e4. So its for sure that we are going to be left with a light squared Bishop. So how can we incapacitate it? Its only after such thoughts cross your mind that you come to the conclusion of 2.Bh7!! b1=Q 3.Bd4 Qb2 and now for the grand finale stroke....
4.Bh8!! black has nothing better than 4...Qh8 and yes you guessed it right! Its a stalemate!!
Conclusion: I think the toughest part of this problem was the move or rather the idea of Bh7!! Well one thing is certain if you solve such studies, you can definitely become more resourceful in your games and unusual ideas like these wont seem unusual any more!!