# Can we say for sure Black's King has not moved?

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

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

The conditions given are "both [White's] castles [=rooks] captured on the same row, Black queen's castle [rook] captured by a pawn, and king's bishop given as odds." The stipulation is that you must find where White's castles [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), then moved back? I do not see "non-movement of the Black king" among the conditions, or anything about Black being able to castle.

• @Glorfindel I don't agree with the edit, as I was quoting Smullyan, who writes 'castle' instead of 'rook' in the problem. – shabbychef Jan 4 at 18:30
• But 'castle' has another meaning in chess, which makes it very confusing... – Glorfindel Jan 4 at 18:32
• I agree with you. Smullyan was mimicking the style of the original Arabian Nights, I believe, writing in an ornate style. I agree with the later edit, however. – shabbychef Jan 4 at 19:08
• @shabbychef I've proposed an edit that I believe contains a compromise (and likely the correct structure for the quote). – user45266 Jan 9 at 3:24

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.

• By the beard of the prophet, I am so embarrassed. I only read through the conditions and then stopped. – shabbychef Jan 4 at 18:26

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 ?

• This is good information for me. However, I simply missed the extra condition, see @Remeilion's answer. Since this book is aimed at an amateur audience, Smullyan is usually very precise, almost pedantic, in describing the problems. For example, in problem 12 of the same book he explicitly mentions that Black can castle. – shabbychef Jan 4 at 18:28
• 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 Jan 5 at 18:27