An Allumwandlung (German for "complete promotion", sometimes shortened to AUW) is a chess problem where, at some stage in the solution, a pawn (or sometimes pawns) is promoted variously to a knight, bishop, rook and queen.
Here is an example composed by Niels Hoeg and first published in 1905. White to move and mate in three:
The key move (white's first move) is f7 (see algebraic notation), 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:
1... e4 2. f8Q any 3. Qe7 mate (or Qf6 mate)
1... Kd6 2. f8Q Kc6 3. Qc5 mate
1... exf4 2. f8R Kd6 3. Rf6 mate
1... exd4 2. f8B Kf6 3. Ra6 mate
1... Kf6 2. f8N exd4 3. Rf7 mate
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. f8Q is stalemate, while following 1... Kf6 2. f8Q Kxg6 there is no mate.
It is regarded as one of the greatest challenges for a composer of chess problems to devise a satisfying Babson task problem, and for around half a century the task was considered to be near-impossible in directmate[?] form.
Technically, the task can be regarded as a form of Allumwandlung with corresponding promotions by fl and white (an Allumwandlung is a problem which contains, at some point in the solution, promotions to each of the four possible pieces - such problems had already been composed before Babson devised his task).
This 1912 problem by Wolfgang Pauly[?] is, as it were, a three-quarter Babson task - three of fl's promotions are matched by white.
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