
Some remarks:
The black pawn on c7 can be cancelled without causing any damage. The white queen can be replaced by a third white bishop, therefore, wQb1 and wBa8 can change places. Moreover, there are possible setups with the wRf1 on f2 and the bNe7 on f6 — but you can't combine all possibilities.
Not many days ago, I read about the HAP (Human/Animal/Pawn) notation. What is that? It's a special kind of chess game notation, which can also be used for chess problems only. It was invented by Mark Tilford.
A move is denoted by just giving the type of unit that makes the move. There are three types of units:
 Human: King (K), Queen (Q) or Bishop (B)
 Animal: Knight (N) or Rook (R) (in the early days of chess, the rook was the elephant)
 Pawn (P) (not considered human for whatever reason)
 Castling: "O" (not revealing whether it's short or long castling)
 Promotion: "P=A" or "P=H"
 Captures (including en passant): "x" followed by the type captured
 Checks: "+" for all check types
 Mate: "#"
 Stalemate, dead position or draw (50 moves, threefold repetition): "="
Using this HAP notation, every chess game can be written down. But, in most cases, different games give the same HAP translation. In other words, you might derive several different games from an arbitrary HAP notation. For example, take this one: 1. P P 2. P H#, the famous fool's mate. There are eight ways of employing those moves, e.g. 1. g4 e6 2. f3 Qh4# or 1.f4 e5 2.g4 Qh4#. Of course, we are rather interested in such HAP notations that belong to only one game each. With a slight modification of the given example, we can fulfill this request with White mating (puzzle #1): 1. P P 2. PxP P 3. H#. Can you find the proper moves?
Some people started composing HAP problems and there is even a homebrew retroanalysis program written by Mario Richter to test those. This is puzzle #2 for you: 1. P P 2. A A 3. H H 4. AxP AxP 5. O HxP# (composed by Bernd Gräfrath, 2007/11/23).
I hope you played a little bit with this and enjoyed it. These are the solutions to the two HAP problems:
1  1. e4 f5 2. exf5 g5 3. Qh5# 
2  1. g4 e5 2. Nf3 Nh6 3. Bg2 Qh4 4. Nxe5 Nxg4 5. OO Qxh2# 
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