Originally posted by heinzkat
The idea is that Black's pawns must have captured 14 pieces; so there is left only one piece for White. Now the King must be on a5 to support the mate; adding a white Queen on a random place (i.e. b5) would not be possible because Black has no last move (where does the black Queen on a6 come from?). With the Rook on b6, Black has a possible last move in Qc4-a6+.
That's what I got, too. The problem looks sound to me - a8 must be covered somehow, and possibilities are very limited with only two pieces [one of which is the King] available to place.