Glossary
A "Last Move" problem is especially interesting if
We count retro-moves in single moves, i.e. moves by one side, so that 1. e4 e5 2. Nf3 Nc6 3. Bb5 is 5 single moves. (The "half-move" terminology has other meanings).
We say a (single retro-) move is completely determined if we know the exact from- and to- squares and which enemy unit was captured (if any). That is, when we know exactly how the board was before this last move. Usually, problems asking for "last n singles moves" ask for completely determined moves.
A recent record-breaking problem by P. Wassong and G. Wilts has 55 last single moves completely determined !
Pascal Wassong (version by Gerd Wilts) Dedicated to Babette
14+12. Last 55 single moves?
Obviously, the choice of potentially possible last moves is larger in Type A problems than in Type B, and in Type B than in Type C. That is why Type A problems are usually preferred.
Here is an example that everybody has already seen. It is a Type B with only one precisely determined last move (reader's exercise: why not the last two single moves?)
J. Mortensen 1956
3+1. What did White just play?
As an example, here is the (so far) most economical presentation of KxN in Type A (to compare with the problem we just saw and which happens to be the most economical KxN in Type B.)
Hugo August, Otto Brennert, Thomas R. Dawson, Niels Høeg and Valerian Onitiu Skakbladet, 1924
4+3. Last move?