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The following position appears as the 7th puzzle of Raymond Smullyan's Arabian Knights, a book about retrograde analysis.

[FEN "3qk2r/p2pp1bp/bpp2n2/8/3N3Q/1PN1P1P1/P1PPP2P/3K1n2 w - - 0 50"]

The conditions given are that "both [of White's] castles [rooks] captured on the same row, Black['s] queen's castle [rook was] captured by a pawn, and king's bishop given as odds." The stipulation is that you must find where White's rooks were captured.

I puzzled over this for quite some time, then gave up. Very early in the solution, it is stated that "Since the Black king has not moved..." However, I do not see how this can be inferred from the position. Is it necessarily true? Couldn't the Black king and queen have moved out of the way of the Black rook (which was captured on e3), and then moved back? I do not see "non-movement of the Black king" among the conditions or anything about Black being able to castle.

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The conditions you gave are incomplete. The conditions include that black (to move) can castle; it's hidden in Smullyan's original problem text.

From the English book, last paragraph of the problem statement:

Just then, however, news came that Black was about to castle. [...]

A clearer problem statement from the Retro Corner:

Schwarz (am Zuge) darf noch rochieren. [...]

Black (to move) can still castle.

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The convention in chess studies and problems is that:

  • Castles are always allowed but if retrograde analysis can prove otherwise, i.e. that rook or king have already moved.

  • En passant captures are never allowed but if retrograde analysis can prove the opponent's last move was the double-step pawn move required.

In Smullyan's problem, if it is possible to reach the position without moving black king nor rook, then you should assume Black still has castling rights.

However, this in itself doesn't prove that the Black King has never moved. Can you show us more of the given conditions and solution ?

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  • The castling and en passant conventions are used for problems with forward stipulations (e.g. "mate in 2"), and indeed originated outside the retro context. These days there are many retros which also have forward content, and many make use of the conventions in various ways. However, in pure retros with no forward content (like Smullyan's), these conventions would serve no purpose, and do not apply
    – Laska
    Commented Jan 5, 2019 at 18:27

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