Mate in 2

White’s aim is clear: shift the d4-knight to threaten 2.Qd4#. But where precisely must the knight land? Of its six possible hops, only one can be the key.

Consider a random move of the wN, for instance 1.Nb5?, but it fails to 1...Rb6!. White might then try the "correction" 1.Nf3?, which provides 1...Rb6 with 2.Ng5#. However, this introduces a new drawback: the g2–e4 line is now blocked, allowing Black to thwart mate on the second move with 1...Ng4!. Note, thanks to the wN on f3, there’s no 2.Bg2#.

This narrows the choice down to two possibilities: 1.Ne6 and 1.Nc6, both preventing 1...Rb6. The first option, 1.Ne6?, threatens 2.Nc5# alongside 2.Qd4#, but again carries a crucial flaw: it closes the e-file, and thus, 1...Nf6! now refutes, since 2.Re7# no longer applies.

Therefore, by elimination, 1.Nc6! must be the key. Black can only counter by manoeuvring either bNd5 or bNe3 to guard d4, and these defences unfold into two parallel sets of variations along orthogonal and diagonal lines:

• 1…Nd~ 2.Rf4#
  1…Nf6 2.Re7#

Any random move of the bNd5 runs into 2.Rf4#, while the "correction" 1…Nf6 is met by 2.Re7# — due to the g6-rook being cut off by the bN.

• 1…Ne~ 2.Bf5#
  1…Ng4 2.Bg2#

Any random move of the bNe3 runs into 2.Bf5#, while the "correction" 1…Ng4 is met by 2.Bg2# — courtesy of the bN shutting off bBh5. 

A neat synthesis of White Correction and Black Correction, orchestrated through Orthogonal-Diagonal Transformation.