Not hard to see what has to be done here, but rather than give the right move, I will show you what happens if black errs:
1. ……….Bg3??
Obviously, black has to move the bishop, and all the moves lose but one- here is a losing one. Continuing:
2. Rf1!
The only winning move- if white doesn’t play this move, black can correct the first mistake. Continuing:
2. …………..Ka2
3. Kc2
Here, 3.Rf3 should also win, but I am pretty sure all the other moves draws. However, study this position after white’s 3.Kc2- obviously the black king has no move since Ka3 drops the bishop to a double ended spear, so white is threatening a two-fold attack on the bishop on the square she moves to along with mate on the a-file. Black will force the bishop to a3 as a shield, then simply leave the bishop pinned while making a waiting move with the rook. For example:
3. ………..Bh4
4. Rf4 Be7 (to get to a3)
5. Ra4 Ba3
6. Ra5 and the bishop is lost
More resistant at move 3 is a move like
3. …………Bh2
Putting the bishop on a square where white can’t both attack it and threaten mate at the same time, but white harasses the bishop, never letting her rest for a move….
4. Rh1
White also wins with 4.Rf2 and 4.Rf3, the latter move not attacking the bishop, but keeps the black king stuck on a2/a1. Continuing:
4. …………Be5
5. Rh5
White wins here with Re1 and Rh3 for the same reasons in the note above:
5. …………Bc7
Guards the a5 square for a move, but white persists…..
6. Rh7
Or wins with 6.Rc5 and 6.Rh3. Continuing:
6. ………….Bb6 (guarding a7)
7. Rh6
Far more precise than Rb7- basically, you get higher precision if the rook can get to a white square on the a-file with the next move- this puts the most pressure on black. Now black has no taxing option- he must either concede the bishop immediately with Ka3, or buy the time to get the king off the a-file by sacrificing the bishop a5 since all the other options are mates in 3 moves or less from here:
7. ………..Ba5
8. Ra6 and white wins.
You should be able to figure out how to get the black king out of his pickle with a better first move.
Well, since no one has posted it, I will finish this up myself. Black can draw with 1. …Be1:
1. …………Be1+
2. Kb3
White must try to keep the white king cornered. On a move like 2.Kd3, black simply plays Kb2 to escape the edge and the latent mate threats- though black probably also draws with Ka2 after 2.Kd3 since he has stolen a tempo towards a3 if white then plays 3.Kc2. However, white is still a move behind a winning position now….
2. …………Kc1!
The only move to draw- if black doesn’t immediately break the opposition in this manner, white again can start harassing the bishop with simultaneous mate threats on the edge. There is no way to keep the black king on the edge now since the bishop still controls the c3 square.
Not hard to see what has to be done here, but rather than give the right move, I will show you what happens if black errs:
1. ……….Bg3??
Obviously, black has to move the bishop, and all the moves lose but one- here is a losing one. Continuing:
2. Rf1!
The only winning move- if white doesn’t play this move, black can correct the first mistake. Continuing:
2. …………..Ka2
3. Kc2
Here, 3.Rf3 should also win, but I am pretty sure all the other moves draws. However, study this position after white’s 3.Kc2- obviously the black king has no move since Ka3 drops the bishop to a double ended spear, so white is threatening a two-fold attack on the bishop on the square she moves to along with mate on the a-file. Black will force the bishop to a3 as a shield, then simply leave the bishop pinned while making a waiting move with the rook. For example:
3. ………..Bh4
4. Rf4 Be7 (to get to a3)
5. Ra4 Ba3
6. Ra5 and the bishop is lost
More resistant at move 3 is a move like
3. …………Bh2
Putting the bishop on a square where white can’t both attack it and threaten mate at the same time, but white harasses the bishop, never letting her rest for a move….
4. Rh1
White also wins with 4.Rf2 and 4.Rf3, the latter move not attacking the bishop, but keeps the black king stuck on a2/a1. Continuing:
4. …………Be5
5. Rh5
White wins here with Re1 and Rh3 for the same reasons in the note above:
5. …………Bc7
Guards the a5 square for a move, but white persists…..
6. Rh7
Or wins with 6.Rc5 and 6.Rh3. Continuing:
6. ………….Bb6 (guarding a7)
7. Rh6
Far more precise than Rb7- basically, you get higher precision if the rook can get to a white square on the a-file with the next move- this puts the most pressure on black. Now black has no taxing option- he must either concede the bishop immediately with Ka3, or buy the time to get the king off the a-file by sacrificing the bishop a5 since all the other options are mates in 3 moves or less from here:
7. ………..Ba5
8. Ra6 and white wins.
You should be able to figure out how to get the black king out of his pickle with a better first move.
Well, since no one has posted it, I will finish this up myself. Black can draw with 1. …Be1:
1. …………Be1+
2. Kb3
White must try to keep the white king cornered. On a move like 2.Kd3, black simply plays Kb2 to escape the edge and the latent mate threats- though black probably also draws with Ka2 after 2.Kd3 since he has stolen a tempo towards a3 if white then plays 3.Kc2. However, white is still a move behind a winning position now….
2. …………Kc1!
The only move to draw- if black doesn’t immediately break the opposition in this manner, white again can start harassing the bishop with simultaneous mate threats on the edge. There is no way to keep the black king on the edge now since the bishop still controls the c3 square.