# A Very Clever Problem

One of my all-time favorite books is Chess Curiosities by Tim Krabbe, now outdone by his website http://timkr.home.xs4all.nl//chess/chess.html.

Chess Curiosities' first chapter is on castling. In the problem world the convention is: if you see a problem where it looks like a player can castle, then castling is legal unless you can prove (by retrograde analysis) that it wasn't but the convention for en passant is just the opposite - you can't capture en passant unless you can prove that on the previous move the pawn being captured advanced two squares. Fair enough. But, as Tim pointed out, several problemists have shown there is a "problem" with that. Here is one of his simpler examples:

Tim writes:
"If White plays 1.Ke6, threatening 2.Rd8 mate, Black castles. Castling proves, however, his last move was g7-g5 [DH: because if Black castles, then neither the king nor rook could have moved before, and g6-g5 is impossible because the white king would have been in check]. But if White accordingly switches plans and starts with 1.hxg6, Black protests that his last move was Rh7-h8. This again proves White could have mated in 2 with 1.Ke6 after all as Black has lost the right to castle, but if he tries, Black again answers 1...O-O, claiming his last move was g7-g5. Which proves that...and so on.
"This leads us to the baffling conclusion that if Ke6 is the key, hxg6 isn't - but if hxg6 is, Ke6 is not. If White attempts one solution, Black has a defence which shows the other would have worked. Or to put it differently again: it is perfectly true g7-g5 and Rh7-h8 cannot both be Black's last move, but White (or the solver) has no way of determining which one was..."

For those who want to see each mate, if Black cannot castle, then 1.Ke6 mates in 2 because the threat is the unstoppable 2.Rd8#. In this case you can't play 1.hxg6 e.p. since, if Black can't castle, it is possible that he could have moved the king or rook on the previous move instead.

If Black can castle, then he could not have moved his king or rook, so en passant is legal and necessary, and 1.hxg6 e.p. will mate next move because 2.Rd8# is still a threat, but if 1...O-O then 2.h7#

So next time a friend shows you a problem and the solution involves castling perhaps, when you have finished that problem, you can give him this one to show that in problems it isn't always so easy to determine if you can castle!

• 16 months ago

Easy puzzle, just look at the FEN: 4k2r/8/5B1P/3R1KpP/8/8/8/8 w - - 0 1

Castling is impossible, so the key is 1.Ke6!  :)

• 16 months ago

Now this is what a puzzle is. it leaves you puzzled!!

• 16 months ago

There is a similar idea in philosophy where to get somewhere one has to first get halfway there and to get there he has to get halfway there, and so on.  It's an idea that doesn't prevent the final destination, but it does put up a potential circular conversation if one allows the loss of the big picture.  Purely intellectual, but fun nonetheless.

• 16 months ago

I tend to think it's rather moot to talk about "what happened before" the position in the study, as, of course, nothing needs to have happened before in a study -- in a study, unlike a game, you don't reach a position; you simply set one up arbitarily whether it could be reached or not. Who says a composed problem even has to be possible to achieve with play?

So it seems plausible to assume that no moves occurred before in a problem because they wouldn't be necessary if you're just setting up the position you want. I guess that would mean castling would be fair game if it fits in with all the other rules.

Because of the ambiguous nature of these kinds of puzzles, as you have demonstrated, I think it makes sense to have it as a convention to tell the solver whether castling is meant to be possible or impossible. If this actually became the convention, then I don't think it would ever give away the point of the puzzle -- if you solved 100 puzzles, with each one hearing whether castling was possible or impossible prior, it wouldn't give anything away because there would be no bias -- whether castling is significant in the situation or not, you would still be told about it.

When it comes to en passant... either deal with the fact that knowledge of it gives away the puzzle or just don't make puzzles like that! Puzzles with an ambiguous en passant possibility mostly just rely on the one simple trick (that you might not consider the move if, you unlike a game, hadn't seen a pawn move before), and don't go much deeper than that. The first time I fell victim to that trick, though, it was cute, I admit. Puzzles where you have to just realize you might be able to capture en passant are like riddles: the difficulty doesn't necessarily rely on the depth but rather the ambiguity of the question, and the exploitation of it in an unexpected way -- often in a riddle, the question isn't answered in a way you would normally answer a question.

• 16 months ago

Retrograde analysis has never been high on my list, but the ideas that you point out here really are thought provoking. This certainly falls well within the definition of curious!

• 16 months ago

Loved this puzzle!