White to move! How should white proceed?
The hard part of this ending comes at move 3 for white.
I don't know right now if white has to take at f3 to draw, but I can't be sure right now that a move like 1.Rf5+ is sufficient as an interpolation- I think it is ok, but I know for a fact that 1.Rf3 is a forced draw (I have seen this exact ending somewhere once before as a problem, but it isn't in my notes. Continuing:
I think other moves will draw here, but this one is most direct- it threatens the remaining black pawn which black must queen to win the game- this forces black's reply:
This is the hard part- there are now only two drawing moves for white, and it isn't immediately obvious which moves they are. Lets look at a wrong one first:
3.Bg6?? Rf2! 4.Kc1
If white tries 4.Kd1, black plays the same as I show below, and if he tries 4.Kd3, black just plays c2 immediately to win. Continuing:
4............Kb3! 5.Kd1 c2+ and the pawn can't be stopped from queening without giving up the bishop.
The key in the line above is that from g6 the bishop can't give check from f7 to drive the black king away from b3 because of the black rook on the g-file. The right moves at move 3 for white are Be4 and Bh7 where, in each case the bishop can give a check if the black king comes to b3 by playing to d5 or g8 respectively.
Black can chase the bishop, but white will always have a move to put the bishop either on the g8/a2 diagonal to prevent the king from infiltrating b3, or on square to check the king if he comes to b3 after the rook drives the white king to c1 by checking from the second rank.
4.Kc1 Kb3 5.Bg8+ and the game is a draw- black can make no progress from here.