Helpmate in 3 (2 Solutions)

The plan here is to arrange battery mates with White's rook and bishop, a common strategy when White has an R+B combination. Consequently, this suggests that c4 and e4 are the most likely squares where the black king will be mated, with discoveries from the rook on the c-file and the bishop on the a1-e4 diagonal, respectively.

One solution is 1.Bf1 Bc6 2.Kc4 Rc8 3.Bd3 Ba4#. The wB eclipses the rook to facilitate the bK’s arrival on c4. Next, the wR wastes a tempo while Black’s light-squared bishop blocks the flight square d3. In the other solution, White's rook and bishop swap roles, with the wR eclipsing the wB, thereby enabling the bK to reach e4. Subsequently, the wB loses a tempo, while the bRa1 (instead of bBh3) self-blocks on d3: 1.Rd1 Rc6 2.Kxe4 Ba8 3.Rd3 Rxf6#.

Note that bRa1 and bBh3's roles are fixed, as each piece is uniquely suited for self-blocking in its respective solution. 1.Rd1 Bc6 2.Kc4 Rc8 3.Rd3 Ba4+ fails to work due to Bxc8 in the end. Similarly, 1.Bf1 Rc6 2.Kxe4 Ba8 3.Bd3 Rxf6+ is not a solution, as the bishop can be taken on a8.