I have to say that I found the problem on the net, found it amusing, but haven't really studied it through in order to find other solutions than the one given. This given solution, on the other hand, is very nice.

Are there other solutions than one alone?

Perhaps the constructor of the problem wanted a minimum number of pieces neccesary to make it a mat-in-one? The solution has two pieces, the king and one more.

Originally posted by FabianFnas Read this posting before my previous one: (I messed it up a bit...)

Yes, white is mating black with one move. Where are white's pieces?
Your suggestion is that we place a king at d6 and rooks at a1 and a2, right?

Then we have this position:
[fen]1r6/krp5/q1pK4/8/1p2p3/1p1p4/Rpp5/R7[/fen]
But this is not a legal position. White has to deal with the king first, it's in check.

Kd6 was a typo, of course. There are plenty of squares where the white king is not in check.

If you remove one white rook and replace it by a piece (or pawn) that attacks the queen, then it works as well. Rook and queen can be swapped too.

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+.