Promotion is happening when a pawn reaches the last row (eighth row for a white pawn, first row for a black pawn) and is transformed to Queen or Rook or Bishop or Knight.
Underpromotion is happening when the transformation is not to Queen.
White plays and mates in 3 moves
The idea in Hofmann’s problem-7 is to show a mate with Bishop and Rook.
Key: 1.e8=B! (If you try to promote to a Queen, you can not mate in the next two moves).
If 1...Kxf6, then 2.g8=R (underpromotion again) Ke6 3.Rg6#
If 1...Kxd6, then 2.c8=R (underpromotion again) Ke6 3.Rc6#
In this problem we observe some similarity in the variations. We say that in the problem there is a theme:
|Theme [Echo - mate] : Two mates in the solution of the problem have mirror symmetry.|
A slightly different situation:
|Theme [Chameleon - mate] : We see two echo-mates, (or we observe the same mate formation) with the king standing on squares of different colours.|
Characteristic 10 : The key is an obscure waiting move, which forces the black to play and create some weakness in his formation, (like self-blocking of the king, self-interference of the linear pieces, opening of a white line, closing of a black line), thus giving a tactical advantage to white.
Note : The moves we make in order to hit our target are called strategic moves. The moves we make, just because our opponent has moved in a certain way, are called tactical moves.
Recapitulating, a key is a threat or a waiting move. On waiting problems white might have mate for every black move during set play (where we suppose that white has played something and we observe the possible black answers), but white must play, because it is his turn to play. The played key might sustain a blocked position (complete block problem) or it might change the mates of the set game (mutate problem).
[This Post in Greek language]