White wins with the absurd-looking 1. Qa5!:

1. … bxa5 2. Bc5#
1. … Kf2 2. Ng4#
1. … Kd4 2. Qc3#
1. … f2 2. Qc3#

If Black moves the bishop, then the queen gives mate from d2. If he moves the a-pawn, then White captures the b-pawn with mate.

“[T]he key move — the queen unexpectedly leaving her strong position for one so odd and apparently weak — is one of the best points of the problem,” Laws writes, “and the general gossamery nature of the mates helps to keep the solver, though perhaps momentarily, off the scent; for when the squares immediately surrounding the Black king are attacked by slender means, the mind’s eye is liable to be confused or deceived, and the difficulty is thus increased.”