Mate in 4

There are two logical tries that must immediately catch the solver’s eye:

1.Rd3?, threatening 2.Rd4#. On d3, the rook is clearly immune, as 1…exd3 runs into 2.Nxd3#. However, Black counters with 1…e5! 2.Re3 (threatening 3.Re4#) Bxf5!, leaving White without a path forward.

And

1.Re3?, threatening 2.Re4#, but refuted by 1…exf5! 2.Rd3 (threatening 3.Rd4#) Qe7!, cutting short White’s onslaught.

These observations suggest that White must prompt Black into compromising one of their key defenders—the queen or the bishop. But how?

The solution begins with the clever 1.Rbc3!, setting up the threat of 2.Rxc4+ bxc4 3.Rxc4+ Nxc4 4.Nd3#. Black can attempt to reinforce c4 with either 1…Qa6 or 1…Ba6, but this plays into White’s hands, as seen in the following variations:

1...Qa6 2.Re3! th: 3.Re4#

2...exf5 3.Rd3! th: 4.Rd4#

3...cxd3 (Now there is no Qe7) 4.Nxd3#

Alternatively,

1...Ba6 2.Rd3! th: 3.Rd4#

2...e5 3.Re3! and 4.Re4# is unstoppable; there is no Bxf5.