The Solution
Sometimes the solution to a problem cannot be deduced by a purely sequential reasoning
process - a leap of the imagination is required. It seems likely that White's queen
will be involved, because at the moment she is not using her full powers, but how
exactly?
1 Kd6! This certainly brings the queen into the game, because it creates the threat
of 2 Qb7 mate, but otherwise it appears to be one of the most unlikely moves on the
board.
Not only does it allow Black's king to flee to b4, it also permits Black's rook to
deliver check on either d3 or g6. However, both these checks block the h7-bishop's
attack on b1, allowing White to give mate by discovery 1...Rd3+ 2 Bd5 mate or
1...Rg6+ 2 Be6 mate.
The only other move to meet the threat is 1...Kb4, but this leads to the third mate by
discovery after 2 Kxc6.