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Allumwandlung (German for "complete promotion", sometimes abbreviated AUW) is a chess problem where, at some stage in the solution, a pawn (or sometimes pawns) is promoted variously to a queen, rook, bishop, and knight. Allumwandlung's main requirement is promotion, either a white pawn or a black pawn. A Babson task may appear if both pawns are spotted in an individual problem, corresponding one another.
The diagram shows a chess problem with Allumwandlung composed by Niels Høeg and first published in 1905. White to move and mate in three. The key move (White's first move) is 1.f7, and depending on how Black defends, White promotes to either a queen, a rook, a bishop or a knight on move two. The lines are:
The importance of White's underpromotions can be understood by considering what happens if he promotes to a queen no matter what Black plays: after 1...exf4 or 1...exd4 2.f8=Q is stalemate, while following 1...Kf6 2.f8=Q+ Kxg6 there is no mate.