Mate in 3

A seasoned eye will quickly spot the one-move mate threats White can pose with the knight on e5: 1.Nc4 threatens 2.Ne3#, 1.Nxd3 threatens 2.Nf4#, and 1.Nxf3 threatens 2.Nh4#. However, in each case, the bishop on a5 comes to the rescue—1.Nc4? Bb6!, 1.Nxd3? Bc7!, and 1.Nxf3? Bd8!.

The challenge, then, is to first shut down that meddling bishop—to cut off one of its lifelines: the diagonals b6–e3, c7–f4, or d8–h4. But how? 1.e4!, preparing 2.Rb1 followed by 3.Qf1#, does the trick. To meet this threat, Black must move the knight from b7, which clears the way for Bxd5+ should Rb1 be played. But here's the twist: that very knight move ends up shutting down one of the bishop’s crucial diagonals, and White is ready to pounce. After 1...Nc5, 2.Nc4! strikes, and there’s no way for Black to prevent 3.Ne3#. Likewise, 1...Nd6 is met by 2.Nxd3!, and 1...Nd8 by 2.Nxf3!, with 3.Nf4# and 3.Nh4#, respectively, now inevitable.

The final point: only 1.e4! works as the key. Although 1.exd3, 1.e3, and 1.exf3 threaten the same 2.Rb1 and 3.Qf1#, they fail due to precise Black replies. 1.e3? is refuted by 1...Nc5!, as White no longer has 2.Nc4 followed by 3.Ne3#. Similarly, 1.exd3? rules out 2.N(x)d3 (leading to 3.Nf4#) and is therefore defeated by 1...Nd6!. Lastly, 1.exf3? fails to 1...Nd8!—the occupied f3 square denies White 2.N(x)f3, and the road to 3.Nh4# is closed.