Fairy problems used to be fun.
Take a position, try to trace
It back in time. There's only one
Last move, perhaps, for some strange case.
In the best puzzles each piece counts,
Some for the places they can move,
And some just in combined amounts.
Their numbers, looking backwards, prove
How many captures have been made,
Which doubled pawns suggest as well,
Revealing more of what's been played.
With this in mind you then can tell
Whether that corner bishop came
Up as a pawn and got transformed.
But in real play, it's all the same.
The curious can be informed
By scoresheets and no one will care
If it had been a pawn or not.
It doesn't matter once it's there.
You use whatever piece you've got.