This page shows "Type D" Last Move problems.
The game is to find diagrams such that the stipulation "Last move? Duplex." has a unique solution (i.e. the last move is determined if White just moved, and again the last move is determined if Black just moved.) The diagram is necessarily check-free.
There are basically 60 different kinds of last move. Therefore, there are in principle 60*59/2 = 1770 possible Type D tasks. This is far too many to be interesting, so different composers have focused on a different sub-themes, e.g.:
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