Retrograde chess problem

This is a "retrograde" chess puzzle. That means that you'll need to think not only about the next few moves, but the past history of the game. The position must be one that could arise in a normal game, played with legal moves from the standard starting position.

Second hint: show

Third hint: show

But Black appears to have a defense to all three: O-O.

Can White castle? Can Black castle?

Solution to metapuzzle: show

The answer to "can White castle? can Black castle?" is: a player can castle if and only if there's no proof that they can't. This is weird and arbitrary, but it provides a unique solution to the puzzle.

Solution to puzzle: show

O-O-O

Where did the two white rooks start the game? There are two possibilities:

They both started as rooks. One of them escaped from the lower right corner of the board by the white king moving. Therefore White can't castle.
At least one of them is a promoted pawn. It must have left the eighth rank via one of d8, f8, or h8. Any of these would involve either the black king or the black rook moving. In all these cases, Black can't castle.

So it's possible that White can castle, and it's possible that Black can castle, but it's not possible that both can castle.

White can play O-O-O, and does. Now Black can't play O-O. Whatever else he does, White plays Rd8#.

Comment: show

This puzzle is from the site linked below. Also on that site are this document and this one, which both support the view "a player can castle if and only if there's no proof that they can't". Both documents were created 50 years after the puzzle was composed.

A retrograde chess problem

Problem statement

First hint: show

Second hint: show

Third hint: show

Solution to metapuzzle: show

Solution to puzzle: show

Comment: show