Mate in 4

The logical try 1.Qh8?, aiming for 2.Nc3#, is refuted by 1...e5!. Instead, the key is 1.Qa1!, quietly shifting to the opposite corner and introducing the subtle threat 2.Nxa3, which paves the way for 3.Qe1+ Kd4 4.Qe3#. If Black defends with 1...Ra7, White then strikes with 2.Qh8!, threatening 3.Nc3#. And now, with the rook deflected to a7, 2...e5 is met by 3.Qh1+ Kd4 4.Qd5#. 

The other defense, 1...Rd4, is elegantly handled by 2.Nc3+ Ke5+ 3.Ne4!—and here, with the rook pinned, Black is forced into 3...Kxe4 4.Qe1#. 

Neat!